1) The first mission would almost certainly be a set of robotic probes (especially in light of recent developments)
2) As controversial as it may be, we could genetically engineer descendants who are better suited for space travel
3) Cybernetics hold the potential to preserve the biological human 'essence' (brain and nervous system) while minimizing the amount of living material requiring maintenance
4) Hibernation is still a possibility, or at least we haven't ruled it out yet
When you're looking at long enough time spans - which we should have available if we manage to avoid extincting ourselves - many more possibilities emerge beyond simply "put a bunch of regular humans as we currently are into a tin can".