The Ruger 10/22 is known for reliability, not target accuracy. It's possible to make them accurate, but that generally involves trading up to a higher grade barrel with a tighter chamber.
The "other" reliable and inexpensive 22LR rifle is the Marlin. IMHO the Marlin is at least as good a gun as the Ruger (maybe better), and it costs less -- but it doesn't have all the aftermarket magazines, stocks, and other gadgets that you can put on a 10/22.
I've had good luck with Aguila, CCI and Winchester. I couldn't do much with Remington. However. . .
Specs of 22LR chambers and barrels vary so much, you can never predict what ammo will perform best in a particular gun. You just have to try different ones until you find out what it likes and what it doesn't like. Your gun might love Remington ammo, who knows? Before you run out and buy 5,000 rounds of ammo, I suggest buying a box of this and a box of that, and test the different brands before you decide what to stock up on.
Standard 40-grain high-velocity ammo works about as well as anything in a 22 rifle. You can get hollowpoints, but they're pretty much useless -- except CCI Stingers. Stingers tear up armadillos pretty dramatically, but they are a bit expensive and their accuracy is lackluster in a lot of rifles.