This may have already been suggested, but I think it'd be cool if you could play as one race, but own the ship of another. For example, if you wanted to be a Novakid, but you love the ship layout of a Floran ship. I don't necessarily think you should just be able to choose your ship right off the bat, though, because it wouldn't make a whole lot of sense to just be flying a different race's ship, but it might make more sense if you could pay to switch your ship in the Penguin Bay.
The same could go for pets, too, I think. I realize that the ships and pets are what give each race its own personality, but I think it could allow for even more individualism if everyone could customize their stuff exactly as they want everything to be.
I hope Chucklefish implements these cosmetic choices for the endgame. I would love to see a return of the old S.A.I.L. personalities in the endgame as well. Different ship pets, ships etc. could be a reward for some endgame quests after the main storyline.