My suggestion would be a 25-06 Remington. Less recoil than a 270 and a flat shooting cartridge. There are many factory loads available with 100-120 gr bullets for deer sized game and 85-90 gr factory loads available for varmint hunting. If you choose to go after large hogs there are loads available with the Barnes TSX & Nosler Partition from Federal.

Most in my camp in SE OK use the 25-06. I'm the odd ball and use a 257 Roberts. I do own a 25-06 in a Smith & Wesson 1500. Using my 115 gr handloads you aren't kicked out of the scope and generally see where the bullet strikes an animal you are shooting at.