The kids in 4-h in our area can and do compete english and western equitation, showmanship, gaming, and some jumping so there is a wide variety of things she could do. That said, she currently rides english and she prefers that to western. She is starting a bit of jumping and seems to like it and her trainer is an eventer, so I think that is probably the path she will take.
As far as training, he doesn't seem to have many specialty skills in place. He understands the basic forward, left and right and he crosses the barns trail class bridge without a hesitation, but he seems resistant to backing up under saddle (does it great on the ground). We haven't tried it yet, but it is doubtful that he knows how to turn on the haunches or the forehand or sidepass. We have been working trot poles with him and he is getting better at them. At first he was very awkward but he has never balked at going over. My daughter's instructor had her do a few cross rails with him last lesson and he doesn't refuse but he more steps over them than jumps. All in all I kind of think of him as a kind and willing but ignorant horse. My question is whether my daughter and I have the skills to educate him.