For $500, you could get an excellent used Remington 700 or Winchester model 70.
.308 is an excellent caliber, but 6MM Remington, .243, 257 Roberts, 7MM mauser, .270 Winchester, .30-06 etc are also excellent.
The problem is a scope. anything worth owning is going to cost at least $250.
The K-Mart blue light special for $149.95 is a waste of money.
And I looked, and behold a pale horse: and his name that sat on him was Death, and Hell followed with him. And power was given unto them over the fourth part of the earth, to kill with sword, and with hunger, and with death, and with the beasts of the earth.