Well for hunting you definitely want a compound bow. I dont think its very responsible/practical to hunt with a long/recurve.
To realistically get into bow hunting, you are probably looking at a total investment of around $500. A decent entry level bow will run you about $275-$350, then you have arrows, broadheads, field points, etc etc.
I would look at some entry level bows from companies like Diamond, Bear, PSE, etc. If you are serious about getting into bows go to somewhere like Bass Pro or Cabelas where they have an indoor range. You should be able to try out a few different models (a lot of times the same model bow will be available in more than one draw weight). Bows are customizable by swapping cheap parts and they're adjustable, but I'd try a few different models out to get the best stock fit before you try customizing it.
I would check out something like this:
http://www.basspro.com/Diamond-Razor...10206144/65967
It got pretty good reviews, its an entry level bow, and its a good brand