I would go with any of the basic offerings from a reputable brand like Matthews, Hoyt, Bowtech or PSE. As others mentioned, dont buy a used bow unless you really know what you are doing. That and you typically need to add $200 to a used bow for new strings and a tune anyway. When you budget dont forget the bow is a small part of the total cost. You still need to get: Arrows, stabilizers, rest, release, quiver, broadheads, bow case etc.
On a side note, dont think of bow hunting as an event in itself. If you really want to do this, you need to love archery and enjoy shooting all year then the hunt is just a way to prove your skills in the field. If you are only shooting for the hunt you will spend a bunch of money, practice all year, get in the field with your tag, not see an elk then get burned out pretty fast. Also, look to see if there is a archery shop with an indoor range or an outdoor range nearby. If you have a place to shoot that is 10 min away you can go all the time, if you have to drive an hour its much harder to keep it up and stay motivated.