
Tarik Blackhands |
Mount eidolons work quite well. Get yourself a longspear or suck a feat/ioun stone to get lance proficiency and you can have a fairly workable build. Of course the way eidolons works you're unlikely to have something that resembles a pegasus for very long if you're filling in its natural attacks.
I'd personally go for a quadruped over a serpent base due to their evolution spreads, but whatever butters your toast in that regard.
The biggest setback to the mounted eidolon is that you're pidgeonholed into playing a Small race or waiting quite a while before the eidolon can be evolved into Large size

Tarik Blackhands |
If you're going to have a medium char UC Eidolon, bear in mind you won't be flying till level 8 at the minimum and your mount will have barely any evolution points to work with (outside of feats, favored class, or eidolon specials, flight and size large consumes all your evo points).
An air elemental base form is probably best for the flying mount. You get magical flying for free, a pretty decent suite of abilities and available evolutions, and are extremely open to being fluffed as needed. Half Elf is probably also a wise race to pick so you can dump all your favored class bonuses into additional evo points.