So we're starting at 15th level, and I'm looking for a strong medium sized mount to use for my Halfling Cavalier. What are some useful mounts and ways to get them?
Depends on what you are optimizing for, but I think that the consensus is that a Boar is probably the best as it keeps medium size and has good bonus all over. You can get one by buying it off a truffle farmer.
If no truffles are around, you are out of luck.
If you don't mind losing some feats, Monstrous Mount can get you a Worg, which has 6 INT and good stats all over.
PS: Get the Indomitable Mount feat if you want your mount to last one encounter.
Beast rider archetype adds the raptor, which is an incredibly good mount with 5 natural attacks, pounce and all around good stats. He can even partyface with 14 charisma
The boar got more survivability though.
At level 15 I'd take the leadership route if allowed and get a monstrous companion or better yet a druid friend.
If that's not allowed going beast rider is perfectly fine so long as you provide your mount the means to fly.
If you're going to take all Cavalier levels then Beast Rider offers some interesting stuff. I'd personally go with the Huntmaster archetype though. That way you can get a Medium sized dog with the Trip special attack, and the dog can share your challenges. This can greatly improve the mount's combat abilities.
If you're willing to take the Boon Companion feat a couple of times you could also have a Bird companion though it would be stuck at 8th level unless you're willing to sacrifice some levels from the Dog. With Reduce Person you could use the Bird as a flying mount when needed. It also might be hardy enough to hang around near combat using Aid Another and Bodyguard.
@Grangerer - If my mount had 14 Charisma maybe I'd have it use wands. I've joked about a T-Rex who uses wands before (that's what those little arms are for!)
@TarkXT - If the DM allows Leadership you could have a cohort in addition to the standard mount.