get a 30-06 in bolt action and that you can afford and you will have a weopon that will last you the rest of your life. You can get used if you are comfortable with your dealer or new if you can afford it. Ruger, Remington, Savage all make decent bolt action rifles. But for 300.00 you are looking at used maybe a Handy Rifle (single shot but accurate)made by New England Firearms would do the trick. You can always trade up later.
Man, I just bought one of these a week ago. Never guess what caliber .... Ok, maybe you could ;-) Anyhow, it was S&W 500 Magnum. $240 + tax.
I'm in love.