Personally I won't look at a horse (for me to buy) that's any smaller than 15.3. And at 15.3 it better be an amazing horse with a massive Stride. I would prefer 16.1-16.3. But that's just my preferences. Since I show/showed in the 3'6 A show hunters (3'9 this year) I need a horse with a lot of step and bigger horses generally have bigger stride (tho now always) plus bigger horse's tend to be rewarded more (could be b/c they can get down the lines on a slow big canter or just b/c the judges like them more)
I also am moving into the 3'6-3'9 jumpers so I want a big stride horse. I find they 'look the part' more too. Big, bulky sexy jumper horses haha.
Please remember that these are just my preferences and I am not saying that smaller horses are bad in any way
I'm about 5'4" (give or take), but I ride a 13hh pony a ton (he is a stinker, that's the only reason I'm riding him). I sometimes ride a few warmbloods (16.3hh, 16.1hh) and get payed to ride a paint gelding who's 16hh and really lengthy.