Personaly I would question the wisdom of buying a jumping pony when you don't know how to jump!
Anyway, When I try horses If they are broken I have a set procedure:
I'd prefer to see the horse caught from a field if possible
I assess the horses conformation and then watch it trotted up for me
I want to watch the owner groom and tack up the horse paying close attention to the horses reactions and to anything the owner is doing that may indicate that there is something wrong.
Then I watch the owner Ride the horse. I ask them to warm up as normal and then I want to see a walk, trot, canter and gallop on both rein and some jumping if the horse is a jumper. I also want to see the horse ridden through movements to the level at which it is schooled so if it is at Elem level I will expect to see medium trot, counter canter and reversing. I also like to see the horse hacked out
Then I will Ride myself. I normaly know pretty quickly if I like the horse and if the horses is as well schooled as advertised. I often spend less then 15 mins in the saddle (the longer I spend the more I like the horse), I knew within 5 mins that I was having Stan (the last broken horse I bought). I can feel when the horse is just unschooled, can be reschooled or just plain awkward.
I like horses that are willing and trying to please and will often overlook a lack of schooling for a horse with the right attitude (I can always reschool a horse, I can't change a horses personality)