It is hard to beat a good 30-30 or 35 REM for deer hunting. The lever gun is a great woods gun but if you have open or long range shots where you live you might be better suited for one of the flatter shooting cartriges.
If you have gun shows in your area you can get a good Marlin for under $300. Ruger, Savage and Remington all have guns in your price range but you will need to decide what type of conditions you will use it in.
Just some thoughts