That first jump makes me nervous. There was really no reason for her to hang her legs so badly. If you wanted her for X-country, I'd say no way. I have a feeling that she's a little more green--or poorly trained--then they let on. I also don't think she has 'great jumping form'--most of the time, it looks like she's 'playing' with the jump and that's the only reason for her exaggerated snap of the legs. Otherwise... she might jump like the first video. eek. (and for hunters... paints don't usually do well if you wanted to be competitive.)
I guess it's just a question of 'how much work are you willing to put into a horse?' She's not going to get any good dressage scores the way she is now, and with her head/evading the bit because of poor hands, it's going to take talented, soft hands to bring her back for any kind of serious showing (other then 4-H).
It also doesn't make sense for you to get a pony at your age--you'll grow out of her and then you'll look awkward--and trust me, a lot of judges won't pin you when your look big compared to your horse! For longevity's sake, I would suggest looking at something a little bigger, so you can keep her. I'll say this for a lot of people--when you get your first genuine horse, you never want to sell that one to 'move up'! (I know I still have my first horse!)
I like her color, though. I DO have a soft spot for paints. But if I were you, I'd look for something a bit bigger, and steer clear of a cheap 'awesome' horse that they clearly can't get sold. There is one truth about this market--bad horses are having a HORRIBLE time in getting sold. /Good/ horses are still going for the same expensive prices!
One last thing--she might not have her height card, which means she may not be a true pony--then you'll just have a really tiny horse, and if you ever did want to sell her--it's really hard to do.