Longer term, and more distant colonization will have to be undertaken by self contained space ships that stop to mine and replenish resources as they go. Maybe they will even duplicate themselves on the way as their population expands, but what would be the incentive to set off in the first place. I would guess it would be private money driven by social, religious or political agendas i.e. groups who could see no future for themselves on earth, much as early European settles migrated to America. A continuous migration of this sort would offer the best long term hope for survival of our species. Many, maybe most, of the ships would be destroyed, but maybe a few would survive to spread the human race to other parts of the galaxy.
Whether the inhabitants, after many generations on board their self contained ships would want to settle on an uncertain planet once they reached their destination is an interesting issue. I would guess that if they saw their new planet as an easy source of resources they would slowly start to colonize it as they realise the benefits of fresh, free air.
Of course, if we had to abandon the earth in an emergency it would be impossible to save more than a small number of humans. Would this be the ultimate lottery? Or would NASA select only those most likely to survive? Or would seats go to senior politicians and the highest bidders (would we want the future of the human race to be in their hands)? Their chances of long term survival would be extremely unlikely. Better surely, to ensure the long term survival of the race, to gradually migrate to the solar system and then the stars? I feel a story coming on here.