You know, I'm kind of annoyed with these questions. Not because they are bad questions, but because people seem to forget what mankind is truly capable of when the chips are down.
Let's start with the ship needed.
First off, ship design. Yes, scale is important, but not as important as a dozen other factors. First, you need something that rotates, to help build up centrifugal force (simulating gravity). Then you need to factor in an insulating layer to protect the inhabitants from cosmic rays, space debris, and other undesirables.
So. Rotation of habitable section. Look at the Ark from Halo for a beautiful example. No, I'm not talking about scale, I'm talking design.
What you could take from this is that circles are your best bet. So the habitable zone of your ship should be designed around this concept. But it also has to be able to reliably fly through space, so how to do that? Well, look around and you'll find dozens of concepts. Just to offer a few:
What you want to keep in mind is two things. One, the ability to dock, take off from your 'mother ship'. So you'll need a section that can counter-rotate so it doesn't screw up the artificial gravity for everyone. I'd advise the second design for that purpose, and make sure to use some kind of logarithmic acceleration/deceleration to make the transition as smooth as is humanly possible. Keep in mind that this section has to be large enough to house several smaller ships for manned and unmanned space exploration. You'll be searching for a new home, after all, and you'd want to minimize risks.
Ship hull requirements!
Something to keep in mind, is the current research done to this end. First thing to remember is space debris. There has been research done that highlights these risks and how to best combat them. Make sure there are thin layers of aluminum to slow down the debris and absorb the kinetic force. Keep these layers separated by some kind of shock-absorbent materials -- I believe the latest was a sponge like material, but it all depends on what you can figure out. Check out: this link and this one for Nasa's current thoughts on the matter for Mars missions (not necessarily pertaining to hull design, but both real-world tech, and more than enough extra information that might well help to further your research).
How about propellants?
Well, there has been plenty of research towards this end as well. In Situ being the more popular, but there have been theories about ionized air being used as well. The problem is that this ejects matter that you won't be getting back, so you'll need to be especially careful with this. I believe the two links from the previous point would prove more useful in this (especially the anti-matter engine proposed), but that isn't yet in our reach to do consistently.
Great, but how do we build the thing?!
Well, that's both simple and complicated. Simple, because it obviously needs to be assembled in space. Complicated because thinking inside the box makes this an expensive means.
Or does it?
SpaceX has been doing research into making it cheaper to do just that -- get materials into low earth orbit, for example. They've designed a rocket that can get you up there, and one that can be reused -- which drives down the costs considerably. Now, if you use the In Situ propellant, combined with this rocket? It would drive down your costs considerably.
Now, once you get your things into orbit, you need to assemble the thing. You can do this the old-fashion way, of sending people up there to do just that. But frankly, that is both costly (you have to pay them) and inefficient (training needed, how cumbersome current spacesuits are, etc) so you're better off with some kind of remote controlled robots to do the assembly for you.
First off, it simplifies things (no need to return them to earth every few months, you can have a team of operators controlling them from earth, and they don't ask for hazard pay). As well, if something happens to the robots, you can have other robots collect them and return them to earth with the next shipment to drive costs down even more. Your project won't get the negative publicity for costing human lives, and it means things can be put on a tighter schedule than it otherwise might.
Ship's built, now what?
Well, with the 'hard part' done, you'll want to test the ship for habitability. So in the next shipment, you want plants for aided oxygen scrubbing, and animals to test if everything is safe for human occupation.
I'd advise taking a variety of both (start with potted plants, rabbits, rats, and chickens). Why? Because the more data you get at this point, the better. In addition to them being there, you want sensors that are continuously tracking air composition, air pressure, temperature levels, radiation levels, and all the fun stuff. If something happens at this point, you're still golden, because it would kill animals, not you and your fellow 'escapees'. Let these beings survive for a year in space. Test effects the environment has on them, and be sure to test your ship in a solar storm (kind of important if you want to survive on the ship for many generations).
And last, but certainly not least: financing the whole thing!
So, we know from other answers that cost is a big thing. So how do we work around that? Well: research. You need to approach many governments/space agencies with a proposition of research. Do not tell them you're building the ship for escape, that's just silly. Say you're a group of scientists trying to prove the habitability of space for humans. Your 'project' is meant to stay in earth orbit, or at worst be a cheap means to travel between earth and Mars (whatever sells the idea better).
Do the scientist thing: produce papers for peer-review based on your findings, play the game for your investors (keep them happy and paying). Then, once you and your fellow 'escapees' feel confident the ship meets your standards, announce that a team will be moving onto the ship for human testing over the course of X amount of time. Once everyone that is meant to be on the ship is on the ship, and you have everything you feel you would need:
Set course for the second star on the right, and keep on 'till morning.