These are currently the top Prix breeds.

Cross Country: Gypsy Vanner
Trot: Peruvian Pasos
Show Jumping: Selle Francis
Dressage: Lusitanos
Gallop: Thoroughbreds

Cutting: Argentinean Criollo
Western Pleasure: Tennessee Walker
Reining: Lipizzaner
Trail: Nokotas
Barrel: Mustangs

Rogin put it perfectlu but I'll also add that in general, TBs can do well in Reining (4th best skill is Stamina), Lusis and Nokotas tend to work for both since very few breeds have trot and dressage in their top 3 skills. It might be easier to get a TB than Lipizzan if you aren't looking to place top 10.

KWPNs used to be the jump breed and a top of line KWPN can still place well enough to be part of a fountain holding lineup. French Trotters are also a good option for Trot. I would suggest that if you're fountain holding on a budget to look out for top GP in non-Prix breeds, since they can also do well and sometimes are cheaper.

In general the Western Prix is also slightly less competitive than the Classical, so if you want to splurge for top Prix skillers they will last longer too. I've seen quite a few horses get T10 placings for two weeks or more in the Western Prix, but hardly the case for Classical.