You'll be hard pressed to find anything decent in the "new" category for that price. Maybe something used either here or in the classifieds on www.archerytalk.com. Or I'd suggest patronizing a local pro shop and see what they can help you with.

If you have no experience, though, you need to find out what draw length you should shoot and what draw weight you can handle. And look for a bow that is draw length adjustable as this may change as you learn to shoot.

Weight isn't a problem. All bows are weight adjustable, usually 10# down from the peak the are marked for. Don't go crazy with draw weight. 60# is enough for hunting anything. Even 50# will do if that's all you can handle. If you get a bow with too much draw weight then you'll be struggling with it while trying to learn to shoot. This is not a good combination. Make it easy on yourself so you can enjoy what you're doing. Brute strength is not what archery or bowhunting is about.