Your ideal candidate would be a horse with impeccable jumping style, well mannered, good mover, big strided, brave, handy, and can jump fairly big.
USHJA International Hunter Derby candidates must be able to jump at least 4ft.
So how would a "Derby" horse be different than just a "regular" hunter or jumper? How are the classes different? Do I understand correctly that "derby" horses are judged on their jumping FORM just as hunters are?
The derby courses are usually a little more challenging than a "normal" hunter course, with more imposing jumps, as well as a few jumps that have higher options for bonus points. There is also a handy round in many derby classes, where tight turns can be a factor.
So the derbies favor horses that are very brave, scopey, and handy. Ideally, you would like the horse to be a great mover and jumper, but movement is not quite as important for a derby horse, since there is no separate under saddle class.