Please be careful. My friend purchased a gaming chair and his CPS increased by 100000% percent and he sometimes clicks so fast his mouse lights on fire. Gaming chairs are dangerous.
I don't own one myself and the all the ones I've heard of and been recommended are upwards of $300 (which is too much to spend on a chair in my opinion), so I couldn't recommend anything within your price range. Sorry :( You might have to be willing to spend a bit more to find a good one, though.