If you're looking for a breed/height suggestion? I think large ponies/small horses (like POAs, Quarter Ponies, the taller Welshes, etc.) 14hh is a great height :).
I'm 14 and I got my POA/QH cross gelding who's 14.1hh when I was about 12 years old. Height-wise, he's perfect and I still fit on him very nicely. Granted - he was 6 years old and still a pretty green barrel pony when we bought him (I don't really reccomend that)... :P
If I were you, I'd look for a good pony who's pretty kid-friendly, (Probably 8+ years old...) in the 14hh range.