For that budget, you can probably hunt anywhere for a really, really nice axis.
I know that Porter's has some real up-and-comers within that budget. But you should have no problems finding a hunt with all your requirements within your budget. Lots of choices.
If you want a real challenging hunt, try one of the outfitters here offer free range axis hunts. There are several here on this board.
I don't think you can go wrong with most any of the outfitters here on THF - just decide on accommodations, type of hunt, and these guys will get you fixed up.
And be sure to let know with pics!