Bolt action is a lot easier to deal with and you get better value and accuracy. Common cartridges would be the 223,22-250,243 for varmint and coyote hunting. 243(minimum caliber in many states,270,7mm-08,308 and 30-06 for deer and except the 243 good for elk,moose,black bear. 30-06 and 308 are probably the most popular hunting cartridges while the 223 is much cheaper to shoot but isn't much more than a varmint/coyote/target rifle. To me the optimal are the 30-06 and 270, wide selection of bullet type and weights, great ballistics and best balanced of the hunting rounds. 308 isn't bad, but I like the long action rifles. Cost of factory hunting ammo for all three of those is equal, and cheap if you buy the bulk stuff from Cabela's or elsewhere.
As for rifles, there are Remington ADLs at WalMart and Cabela's currently under $500, some at close to $400. I've seen Savages today for $377 at WalMart too. A Stevens is $315 everyday price at some places,they are a Savage entry model. Howa 1500 / Weatherby Vanguards are a great value and are usually Les than $500;in fact the Howa 1500-Hogue-Nikko Sterling scope combo is $495 retail and normally a little less. There are some real bargains out there if you look around. Handloading comes in handy---I saw a Browning 223 WSSM for $515 brand new this afternoon.
I've been hunting in Idaho since 1973. I currently reload for 223,243,30-06 and 300 WSM.