So you want an uplift package
Well, there's a lot of work that needs to be done. Now, technological development is not a straight line; there's a lot of things you can forgo and bypass, if you have specific goals, but let's just say we want some of our modern conveniences and see how far we can get.
TL;DR: you can get most of what you wanted, after a fashion, but not on today's level in 50 years.
Let's start out by listing who we need. I have the good fortune to be teaching (and researching) at a technical university, so I'm going to base my estimates on the type of requirements we have for our graduates.
Here we have to stop for a minute and examine our basic assumptions; the first question is whether you get to pick who exactly you get to take back. If so, we can reduce the manpower requirements immensely, if not, you need to take enough people that you will get the required expertise by random chance. I'm going to do an ass-pull and estimate that about 1% of the population have the required skill on a required level, so if you're sampling randomly, multiply the numbers by 100. On the other hand, the extra people with modern education would also help, as you could send them off to do some less complicated tasks.
Let's also assume that the entire population of the area is at your beck and call and will provide their work and whatever expertise they have per your instructions.
I'm further going to assume that the area you're in is something like Europe, since that's where I'm from and it will make things easier on me to have a geographical point of reference.
That said, here's a list of people you're going to need:
To get pretty much anything done or built, you're going to need steel. Tooling steel for things that make things, stainless steel for industrial chemistry and the like. Right now, we're in the bronze age, so people from the more advanced localities (eg. Greek city states) know something about smelting and alloys; your guys will need to teach them to make steel.
Fortunately, iron ore is abundant and coal is not too hard to come by either. Unfortunately, to get good steel you'll need to get picky about the ore and the additives you use. Bottom line, you'll quickly be able to produce some steel, and later you'll use that to make yourself the tools to make better steel, repeat ad nauseam.
This iterative principle is something you'll be seeing a lot of. Using modern knowledge, we can get the development started and get it running pretty well, but the later steps will get progressively more difficult. Whether 50 years is enough time to get to 21st century levels is anyone's guess; I'd say that in this case, and probably most of the others, you can get to 19th/20th century levels before the process slows to a crawl.
2. Civil engineers
This bunch you'll need to make useful things out of the steel you now have. Mostly tools, then fabrication machines, engines to drive the factories you'll need (powered first by water and wind, later by steam as you can machine pistons) and ultimately the tools to make our desired goodies.
They will also be building things; as a side effect of this enterprise, you'll probably be building a transportation network, so there will be roads, ships and barges, wagons, and such. A logistics expert would help here, but you could also just brute-force this.
When your builders aren't busy, you can have them build aqueducts and sewer systems. You'll probably end up building cities around your eventual factories and it would be a good idea to get them some basic sanitation; cholera epidemics can really set you back.
These guys will also be of use when you're digging mines to get further raw materials, and on their downtime they can be designing the thousands of tiny conveniences that will make your life a little more bearable.
The nice thing about civil engineering is that if you have underlings who can follow instructions, a single engineer can get a pretty big project done. After all, that's how it was up until the late 19th century, when we finally ran out of the big projects and more specialisation was required from that point on.
These you will really need to get anything done. Most material science is based on chemistry, so you'll want industrial chemists to design the processes that fabricate your silicon, fuels and whatnot. A petrochemist will be required and a geologists wouldn't go amiss for prospecting.
Some of your chemists should also be pharmacists; an unmedicated black plague can really put a damper on things and you want to get your hands on - at least - some antibiotics and vaccinations soonest. Yes, penicillin is just bread mold, but it's pretty much impossible to tell which bread mold it is without testing (otherwise you could just as easily poison your patient) and you want to be able to produce it in quantity.
Of course, most of this work will require stainless steel vats to produce anything usable in quantity, which is why I listed metallurgists and civil engineers first.
Another important thing that you can get your chemists to do are artificial fertilizers. If you have some guano at hand, you can start from that, otherwise you'll need to first implement the Haber-Bosch process. If you do this, however, you'll also have your first ingredient for high explosives, which will come in handy later.
4. Agriculture experts
Now, farming does not directly contribute to your goal, but it is necessary to keep your working population well fed. Increasing yields by improving your crop breeds and judicious use of fertilizer and pesticides (as soon as you can get them) can make sure a famine will not wipe you out.
Furthermore, before the Industrial revolution, a significant fraction of the population (80% probably isn't far off) had to work in agriculture just to support what population level there was; improving yields not only staves off famine, but frees up a significant workforce that you can employ elsewhere.
5. Electric engineers
Eventually, you'll have to introduce electricity (if you really want to run those computers, that is). These people will be there to build some power plants for you, design and run the power grid a build engines (or, for instance, furnaces) that run on that sweet electricity you now have and can be used in your factories and elsewhere. Electric engineers can also help you with telecommunications, which can help increase your industrial output by improving coordination.
Of course, for most electric machines, you're going to need at least some copper for conductors and rubber for isolation (this can be replaced by layered silk or in some cases resin, but you want rubber for best effect), which your metallurgists and chemists need to take care of first. With these, you should be able to churn out some late 19th century engines and appliances pretty quickly.
6. Computer engineers and mathematicians
I am lumping these into a single category because there will be a lot of overlap in what they will be doing, at least initially. Counterintuitively, computer science is not all that dependent on computers (that is, electronic microcomputers that we know today). The same theory applies to mechanical computers, or even human computers.
Now, you won't be playing World of Warcraft on any of these just yet, but any ability to perform more complex calculations is going to help; many of the folks above are going to be relying on calculations of their own, and the more of those they can make more precisely, the tighter they can make their tolerances. This can in turn decrease costs and/or improve results of whatever it is they are doing.
Keep in mind that at this point, you're not just without electronic computers - you don't have any calculators either, so any time you need to use the value of pi or e, or calculate a sine or a logarithm, you have to do it the old way, which is, consult a table.
Of course, the more precise you want the result to be, the thicker your tables get. It was not entirely unusual to have multiple volumes of just the logarithmic tables, the logarithm being quite important in the pre-calculator era. Aside from that, tables of random numbers might come in handy, and ideally you want to avoid producing all of these by hand, as this is fairly error-prone. This is in fact the problem the Babbage engine was meant to solve, so you can build something like that in the meantime.
Statistical analysis might also be useful in managing your new industrial empire, and computer science is also used to improve telecommunication by developing codes (to compress information or protect it from transmission errors) and ciphers (to keep prying eyes from reading it).
As for computers themselves, you can start building some as soon as you have reasonably precise mechanics, and then transition perhaps to hydraulics, and finally electronics as you can manufacture them.
What about the goals?
Well, let's walk through them one by one.
While I'm pretty confident you can have computers, even programmable ones, fairly early on, you are not getting a 2014 laptop within 50 years from scratch. It might be possible to design it, sure, but the big problem are going to be semiconductors and transistors, which require a lot of advanced manufacturing. Even once you have those, the speed of modern computers is achieved not so much by design (though that helps a lot), as it is by making the basic building blocks really teeny tiny - this shortens the so-called "critical paths" and lets you set a higher clock speed (if you just go ahead and set a higher clock speed anyway, you start getting errors, because all the circuits do not have enough time to appropriately change their state in response to the input).
So I would say you should be able to get electric computers (picture ENIAC), and that those will help, but even with semiconductors, the best you'd get, by my most optimistic guess, is an 8086. The more advanced stuff would be on the way, but would require too many additional "iterations" to fit in your timeframe. Then again, browsing stackexchange probably isn't going to be a priority.
Any good surgeon with a couple of tools can perform a kidney transplant in field conditions (with some luck, the patient might even survive). To do this the proper way from scratch, you'll just need some sterile tools (preferably made from surgical steel) and a couple of chemicals (disinfectants for starters, and if I were to be the patient, I would hold out for anesthesia).
The problem here is making it stick. Even if you find a "compatible" donor, the recipient will likely be on immunosuppressants for the rest of their life. Otherwise, their body will reject the kidney and they will die painfully. These are fairly advanced drugs, and I dare not hazard a guess on whether you can get them in 50 years, but perhaps you can get something more rudimentary that could also work. You might also luck out completely and have no symptoms of organ rejection; basically all the better drugs will get you is a higher success rate, so when exactly you can say you can perform a kidney transplant is rather nebulous.
This is probably contingent on having reasonably fast computers and other electronics to operate the mass spectrometer someone else mentioned. I'm leaning towards "no", because of the above answer on computers.
As soon as you can make gunpowder (which can be fairly early on, depending mostly on whether you have sulphur available) you can start launching rockets. Build one that's big enough and you can try launching an artificial satellite. There are just two minor caveats:
Initially, most of your launches will end in explosions. This will improve as you are able to make more consistent gunpowder, so you can build bigger rockets that maybe don't blow up more often than they do, and eventually you might get into space. Other solid fuels will gradually become available, but liquid-fuel rockets, which get the highest efficiencies, require cryogenics and (essentially) super high-speed plumbing, so you will only have those available fairly late. Solid rockets, however, are enough to get you into orbit (in fact, in the early 20th century, there was a pretty well thought out proposal to ride a solid-fuel rocket to the Moon), if you can get over the next obstacle:
Guidance. By machining the rocket really carefully and balancing it and installing stabilizer wings just so, you might be able to get it to fly in a straight line. However, what you really need it to do to get into orbit is to perform a maneuver called the gravity turn; basically, it needs to burn straight up for a while and then horizontally a lot longer, and you need to build it so that it knows when to do that, when to separate stages, and so forth. This requires a guidance system (staging might be accomplished with a series of fuses), which was a technology not perfected until about the sixties. This is, incidentally, the reason why V2 missed its target more often than not: their big issue was precisely the guidance system. These days, rockets process input from a plethora of sensors and calculate corrections on the fly. You might be able to get away with a clockwork mechanism that performs preprogrammed steering at preset intervals, but this sacrifices the ability to react to changes, meaning again, you will crash and burn quite a lot. But, develop a good closed-loop guidance system (and the sensors to go with it), or launch enough rockets with a simple one and you will eventually launch an artificial satellite.
What good it will do without advanced electronics on board is another question entirely.
nuclear power plants
Getting a nuclear reaction running is fairly easy. All you need is a bit of fissionable material (say, some convenient oxide of U-235), some moderator (regular old graphite will do). Mix these up and make a big enough pile, and you have a chain reaction going.
What, you want to control it?
Oh well, that will require a more advanced setup. You need to encase the fuel in good inert rods, so you can better manipulate it (=metallurgy), do the same for the moderator and also throw in some regulator rods, if you're the safety-minded type, attach all of these to a mechanism that lets you manipulate the rods and you have a reactor. To make it into a power-plant, you put the entire setup into a boiler and use the generated steam to drive a turbine. Connoisseurs will note that I just described the broad strokes of the Chernobyl setup, but once you get the knack of building these high-pressure vessels, you can go straight to the safer pressurized water reactors.
The above glosses over the important point that fissionable material is really fricking hard to isolate. You might be able to mine some uranium in Bohemia and chemically purify it from the ore, but separating the isotopes is usually done in huge centrifuges with really precise control, which likely require electricity and probably also electronics. Once you can build a turbine and a generator, you can start using coal or water power from electricity, which solves the bootstrap problem, but that just lets you start on the path towards nuclear power.
Furthermore lot of a nuclear power plant is the various control electronics, which might be more complicated to develop than the nuclear fuel itself; but you can ultimately make do without them, if you relax your safety requirements enough.
Still, seeing as you will not be needing so much power to warrant working through all these issues, you will probably look for electricity elsewhere
So there you have it! As a final note, there is also a bunch of other technologies that pretty much anyone from the modern times can "invent" if they are so inclined, and another thing to keep in mind is that you will probably end up with a very different overall setup than what we have today. Still, it is good fun exploring these scenarios.