You should definitely look for something a bit bigger, if you're looking to be competitive in the jumpers and if you're looking to jump higher then 2ft, then look for something that will have an easy time carrying you.
Thanks guys I called them to ask about training and such but no one has called me back. I did go look at a larger ottb last night but he has NO training at all and they want 3500. Once I find one that meets my price range and fits me lol I will have a vet check. I feel like if I am spending that much they shouldnt mind a vet check and xrays. I am going to stick with somthing a little bit taller like 15.5- 16h cause my legs are really long.
You should definitely look for something taller if you're 6'1. I'm 5'4 and I have a 16hh dutch warmblood who I think I fit perfectly. (I would say a medium barrel). Here's a pic to compare:
And just to help, there's no such thing as 15.5 hands. It would be 15.1, 15.2, 15.3, 16.0 etc. If I were as tall as you I wouldn't look at anything under 16hh for sure. If you have long legs try to find something with a round barrel. Warmbloods are great for that but I'm not sure if that would be out of your price range or not.
I am 5'6" and I look big on anything under 15hh. If your 6'1" you really should probably look at something around 16hh. The rider is jumping way too high on the neck. The fact that a 4yr old is jumping that doesn't bother me, it's the fact that a young kid is riding and he's being used in a lesson program. That means this horse probably has alot of issues and holes in his training. For the price, you could find something alot better.