i think the resources involved would be enormous.
what you have to realize is that not only would such a ship be very expensive, but at the kind of size you're considering, would most likely have to be constructed in space. therefore, the fuel costs, just to shuttle the raw materials and laborers back and forth, would be substantial in and of themselves.
given that any possible planets are more than likely 100's of light-years away, one would need to accelerate the ship to a fairly high speed just to keep the travel time within the projected service life of the space-craft.
then there are design considerations. if the occupants aren't frozen (and again, a fully automated piloting to an unknown planet doesn't seem like ALL that good an idea) or in some other kind of stasis, then the life support systems will consume enormous amounts of energy, and also increase entropic effects such as corrosion, electrical failure, etc. that over the course of what may be centuries, could be devastating. the amount of redundancy in the design necessary to overcome such obstacles could make the cost prohibitive. it's all very nice to think of creating a nice comfy park-style eco-system, but we don't have anywhere near the technology to sustain that kind of thing for centuries.
and if we did, why bother going to another planet? why not just park it near the moon?
of course, if the planet we live on was approaching uninhabitability, we'd certainly be motivated to undertake such a task. choosing who would go, and who would not could get ugly. and people, being what they are, are likely not to see the necessity of such an undertaking until far too late, with perhaps the unfortunate result of a substandard effort, resulting in utter failure.
the politics of such an undertaking, even if under the best of all possible circumstances, would be a delicate affair. it would undoubtedly be a drain on the world economy, it is likely many then-current residents of Earth would resent the economic hardship they were enduring in order to make it possible. and full-scale testing would not be feasible, meaning fatal design flaws and/or sabotage would be real concerns.
my personal feeling is that, without outside intervention of some knd, the human race will cause its own extinction, and so slowly that they do not take its prevention seriously enough until too late. and my prediction is that this will happen within the next 400 years or so.
but, in a happy world, where sane and far-seeing people carry the day, perhaps we will successively do this. i still feel it will end badly. our biological make-up is strongly tied to this environment, and there are so many subtle ways in which a seemingly accomodating planet could doom us, as well as the obvious ones: toxicity, disease, climate, and unforseen stellar events. with a small enough gene pool, even that could do the new settlers in, not to mention what even a slight gravitational variation could do over centuries. i just don't believe we could evolve fast enough to adapt to another planet, unless it was a very close match to earth.