You're stuck at that crappy spot in the teenage years, where you're too big for an 80, on the small side for a 125, and still growing. A KX 100 would be one option, or you have to learn to deal with riding a bike that is a bit on the big side in the 125. For the money you're looking to spend, a 125 would likely be a better choice, as you can get a better bike for that budget. The 250F's are a bit new to have dropped to where a good one can easily be had for that kind of money. You're likely to end up with problems with one fyou can find given your budget.
If you did want to race, the age limits for the classes could pose a problem if you did go with a 100, as depending upon the rules you're racing under, you might be too old for the 100 class, and forced to race it against 125's and 250F's.