A .223 will feel more like your hunting rifle (more recoil, probably a heavier gun, etc) and it'll still be cheaper to shoot than even a .270 or .243.
As for practicing at the range with your hunting rifle, if you want to be any good at all you need to fire hundreds of rounds from a variety of positions - prone, kneeling, sitting, over a low barrier, over a high barrier, around the side of a barrier, etc., because you never know what field condition you'll be in when you sight your target in the field. Unless your hunting will be strictly limited to sitting in a blind shooting at whatever wanders past, you really should be familiar with shooting from any position. That takes practice, and you'll wear out your shoulder, your gun, and your wallet if you use your primary hunting rifle to get that kind of experience.
So get a decent gun that is cheap to shoot, either .22 for the cheapest way to practice, or .223 for cheap but with enough recoil and noise to help keep you from flinching when you fire your hunting rifle. Wear it out. Shoot that sucker until it needs a new barrel. That way you can buy a hunting rifle that fits your desired game, not something that you will be using both for practice and hunting. If you will NEVER want to hunt large game, by all means get something small. But if you want a more flexible round that can be used for a wider variety of game, get something more powerful. Take it to the range and fire a handful of rounds through it each trip after you're done firing the cheaper practice rifle. That way you build general skills cheaply, and maintain familiarity with your hunting rifle without breaking the bank or your shoulder.
There are tons of neat .223 M-16 / AR-15 knockoff sporter rifles on the market and they're fine guns, but they all seem to be a bit pricy to me and when you carry them around in the field the BLM and other govt goons tend to jump straight from "hi" to "you're a terrorist, give me your gun" even when it's perfectly legal. There are plenty of cheaper .223 rifles out there that shoot just as good, cost less, and won't trigger the federal busybody patrols into panic mode.