See if there's a place near you that sells bows and has a range so you can test them, look through the economy bows and used bows.
Find what fits you and your price range... if you can get some degree of consistency out of a $200 - $300 dollar bow when you're just starting out, it will kill an animal just as dead as a $1000 dollar bow, provided you can hit the target. You shouldn't need to break the bank to get into bowhunting.