The .243 works very well on deer size game. With a 100 gr. bullet it makes the ultimate deer rifle IMHO. With a shot thru the lungs, they don't go far, and a shoulder shot will usually take them down on the spot. Several of my family members and friends use it. The ammo is available at most places, the gun is accurate and recoil is mild. If larger game is in the future for this gun, you might consider the .308, it is a very capable round for overall use i.e whitetails, mule deer, elk, black bear, etc, and is my favorite larger round. If you come across a rife cambered in the 25-06 in you price range, don't overlook it. The 25-06 adds a little more range and moves up a little in the size of game.
In the price range that you are in, I recommend the Salvage or look around for a clean used Ruger 77, Remington 700 or Winchester 70. NEF makes a single shot .243 which would be in your price range. I've had several NEF's and they were very accurate, although never had one in a .243.
Most important, get out there and enjoy the experience of deer hunting. Good luck, hope the thirty-pointer walks into your sights.