Hi Cody,
$500 will get you a OK second hand compound, not sure about recurve (as I don't shoot them).
You will be asked when buying a bow:
Left or right handed bow- It sounds like you need a right handed bow (you hold in your left and aim with your right)
Draw length - Bow Sizing, Draw Weight, and Length - Hunter's Friend Archery
Poundage - To hunt on DOC land you'll need: Minimum drawing weight factor 15 kg (35 lb) The link above suggests that 55-65lb would be suitable for a medium framed man but I think without proper form you might end up hurting your shoulder or something.
I'd really recommend joining an archery club or doing their beginners course if you can before you buy. The benefits being, usually a club will have a bunch of bows you can use and get your feeling for the sport along with practical advice on how to shoot consistently. Someone might even have a bow to sell or lend you.
If you want to hunt sooner rather than later a compound will be the way to go as they are easier to shot further distances accurately.
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