What you're essentially asking is how best to bootstrap a civilisation. To build computers, for example, we need microchip manufacturing, which requires tools and computers of its own.
In some respects this is a similar effort to getting to this point in the first place - the systems and structures we have are those needed to produce what we produce. The only difference is the foresight of how certain things can pan out and what the technology can achieve.
There is a concept in computing of bootstrapping; when you switch a computer on, some very low-level and rudimentary circuitry has to switch on and send the right signals to a more complex chip, which can then load some basic system which works out what the next step to follow is, and can prepare for the next layer of complexity. The process continues until you have the full operating system running with all the setup and machinery it needs.
In a similar way, this civilisation might know what it wants to get to, but to do that it has to work backwards to establish how to get to that point.
Coordination is hard
Enormous projects like recreating civilisation take large groups of people a long time, so to prevent something going horribly wrong in that time, you need a stable society. Stable societies are made of happy citizens who are free to lead fulfilling lives, or alternatively of populations controlled by manipulation, fear, etc.
So the sheer scale of the task not only demands the technical/technological path to be set up, it also demands the social structures and cultural norms which support the environment in which that can be done.
But coordination, leadership, politics, social cohesion - these are hard things to get right, particularly in the aftermath of such an event. So other structures which permit a society to curb destructive behaviour are also necessary - police to whom violent force can be delegated, judiciary to whom legal decisions are delegated, a legislature to whom control of the law is delegated.
Stable social structures
The most stable social structure seems to be a liberal democracy, certainly from our viewpoint in the West. We have tried feudalism, monarchism, dictatorships, democracy with a class system - all seem to suffer from the flaws of being too sensitive to poor leadership, power struggles, corruption.
In a tiny world such as that described, where there is little to no external threat, the political focus would be internal, which tends to result in factions, divisions and power struggles. In authoritarian structures that is dealt with by squashing all rebellion, until a revolution comes along. In a liberal democracy, difference is permitted as far as it doesn't threaten the democratic system itself.
Perhaps the largest difference in human geography would be that there are (at the beginning) no other inhabitants. Similar to humanity's original spread out of Africa, it would be feasible for dissenting groups to split off and settle newly discovered areas. Depending on the timescales involved, this would likely recreate some of the same territory disputes we see today; conflict and even outright war over control of some area or another between groups.
On the other hand, exploration would yield materials and resources which would of great benefit in the effort to reconstruct the tools of an advanced civilisation.
How long will it take?
Assuming all goes fairly smoothly, no world wars, no disease wiping everyone out etc, maybe 1-2 centuries? The main issue of the timing is the construction of tooling; to make a chip you need a semiconductor wafer, for which you need probably silicon, for which you need chemistry labs, glassware, metals, and so on. Having the sum of human knowledge will make that far, far easier and predictable, but you still have to get the minerals out of the ground, extract the materials, manufacture the tools, etc.
It's a bit like going through a chain of DIY videos: How to make your own generator -> How to wind your own electromagnet -> How to make your own wire -> How to smelt your own copper -> How to mine your own ore... But each of those processes is made more difficult by not having the tools to start with. How do you mine ore without a pick, shovel, dynamite? How did ancient Britons mine Tin -> How did early humans make tools...
The kindly aliens
There is one key variable which would make the bootstrapping easier: being given some basic tools by the saviour aliens. If you have the means to cut down trees for wood, mine the earth for ore, drill for oil, then you don't have to go through a painful phase of bootstrapping the tools themselves, and can get on with building up the layers of technology.
Incidentally, I suspect the shorter the path from start to advanced technology, the more direct the route will be - it is easier for a population to focus on a collective goal which is within reach. A goal which your grandparents set for society and which is unlikely to be reached in your own lifetime would likely seem distant and uninteresting to young adults who have other, more pressing, priorities.