Dan is right. Finding a new bow for under $300 that are top quality will be a tough task. Then you will have to purchase sights, quiver, arrows, broadheads, release, and a stabilizer. All to the tune of another $2-300 min.
Look at the package deals that some brands offer. A friend of mine got the least expensive package that Bear sells for $399 a couple years ago and it wasn't too bad but it needed a few extras to make it a good bow. Go to Youtube and search reviews for the Bear Outbreak and the PSE Stinger3G. Bass Pro has them in an affordable package. You will still have to drop another $200+ on arrows, broadheads, release, and practice targets.