Worry about the rifle, not the cartridge it's chambered in. Killing power is much more determined by where you shoot the animal, and the specific bullet you choose to use, than by the cartridge you choose. Pick the rifle that feels best, fits best, and fits your budget. Then I would recommend you go with a cartridge that is one step down in power from what you were considering, such as the .270 Win, and use a GOOD BULLET. I would go for a 130gr TTSX and call it good for hunting. Pick up some cheap 130gr bullets for practice.
The Ruger Hawkeye All-Weather is a great, durable, tough rifle. Accurate, too. The Win 70 is another great. Rem 700 is the Chevy 350 of rifles. There is a plethora of aftermarket upgrades and replacement parts available for these rifles, and the rifles tend to be fairly accurate and durable, as well. Those would be my top picks for a mid-priced rifle. The T/C Icon seems decent, but it's fairly new on the market and weighs a bit more than the others, if that matters to you.