That might have been an option of an alien race that comes here on a rogue asteroid. But for us, it is a waiting game. If we knew that we can't go any faster in the future than we can now, starting early would be useful. But if we can see faster propulsion down the pipe, it is worth waiting, because a later started, faster ship would catch up to, and overtake the slower one.
Meanwhile, we could test and improve on our ability to live in space and use the resources of the solar system.
All fair enough, but maybe there's no time to wait, say if the home planet threatens to become uninhabitable in some way? Maybe a section of the population wants to get away, like the pilgrims? Perhaps we can sell the idea to <insert most disliked category here>.
And I agree that developing this solar system would probably be a first step.
Constructing new ships needs resources. We have them here, and they are most probably in every other system. But there is nothing on the way. That's why I don't think shooting for other stars is useful until we can get there in about three generations.
Yes, that would probably occur in a solar system. Or maybe they could "tow" an undeveloped asteroid to work on during the long interstellar journeys.
I wouldn't put a limitation of generations on it. To someone who is part of a generation that was born in the asteroid, it might not matter how long there was to go, they will never get there anyway. Maybe they would be perfectly happy to just be "space people".
Star Trek has a military/naval command structure. I always thought that to be unimaginative/anachronistic.
Maybe there will be different systems for handling navigation (which only really happens at the start and end) and for the community?
Not military, certainly. Too rigid. In any case, Star Trek people only spent a limited time in space, and we don't know (do we?) what the politics of the home planet were. I would think that the greatest challenges might be maintaining interest in life, as most of the things we worry over would be handled by the automation, and education to stop them dropping back into some non-technical state. I haven't mentioned population control, which would be essential.