The best advice that anyone can give you is to head to a local reputable pro shop. Have them measure you for draw length and draw weight then tell them the price range that you are looking at. If $300 includes accessories then you may run into somewhat of a problem as there are only a few model bows, plus accessories, that will put you at around $300. The PSE Nova would be a good example of this. You can usually get them in the $170 to $190 range. Throw in sights, rest, quiver, release, arrows, broadheads, etc... and you can probably keep it under $300. Ofcourse, some of those items, like broadheads, you won't need until later in the year so don't worry about getting them initially.

Get a bow to fit you correctly and the job is halfway done. Hope this helps.