You need to define "small game" to get any good advice. I wouldn't shoot even a coyote with a regular .22 because of the chance it won't be a fatal shot, but as noted before a .22 is fine for rabbit and other small animals. I also like the 10-22, and you can buy pretty cheap kits to make it a lot more accurate. There are aftermarket stocks, barrels, and trigger kits that can let you really customize the gun for whatever use you have for it. As an example, a stainless 10-22 with a mild bull barrel, custom trigger, and composite stock, can make a great all-weather varmint or very small game rifle accurate enough to hit a rabbit out to 200 yards.
A hunting rifle chambered in .223 will take game up to small deer and can be more accurate than a .22 especially beyond 100 yards, and the ammo is still fairly cheap. AR-15 lookalikes will be very expensive, but there are other less hyped .223 rifles that would do just fine and won't cost as much.
Avoid a mini-14 for hunting unless you intend to take close-range shots only. They are not known for their accuracy even factory new, and making a mini-14 more accurate will cost just as much as buying a more accurate gun to begin with.
AR-15 (M-16) variants are quite often very accurate, but the cost is typically more than double than a regular hunting rifle.
If you want to shoot deer and larger game, you should get something beefier. Realize that picking the gun and picking the type of ammunition are two separate issues... Some guns are only chambered for certain rounds so if you fixate on a particular round, you might miss out on the chance to own a really good gun that just happens to be chambered in something else.
This article discusses bullet size/weight relative to the type of game you're shooting:
http://www.chuckhawks.com/hunting_bullet_guide1.htmI personally decided to buy a browning a-bolt chambered in 7mm remmington magnum, because that combination can take everything from small deer (with a lightweight bullet) to elk/moose (with a heavier bullet) and is quite accurate out to 400 yards or more straight from the factory. The downside is that premium quality rounds cost about $3 each and I don't reload, so every time it goes bang it costs me $2-$3. Compare that with my .223 mini-14 (bought for practice, plinking, and varmint hunting) which costs about 10 cents per shot.
I own a 10-22, a mini-14, and the a-bolt. My brother owns an olympic arms AR with the A2 design and a heavy barrel. His AR completely outshoots both my 10-22 and mini-14. When he got back from army bootcamp, I saw him nail a running jackrabbit at 50 yards, and I personally shot .7 inch 5-shot groups at 100 yards from a simple sandbag rest with his AR. My mini-14 shoots 3 to 4 inch groups at 100 yards and I'm told that is "typical" for a mini-14.
