Then it takes me a while to get around to actually installing it and then finding that it is not all there. My own fault, but it is not like I buy it off ebay or craiglist. Heck, I last bought something for this gun before I ever found those sites.
I bought a Bushnell Sportview 3-12X , 40mm lens, adj. objective. It had a retail price of about $90 but I found it on sale for $60. It does not focus at close range. It's acceptable for 25 yard shooting but the crosshairs fade out at 50 feet. THere is a huge parallax error of about 3" (at any and all distances) that is not at all treated by turning the A.O. front lens. Now at 100 yards, a 3" error is not that big of a deal, considering this is just a factory gun with a cheap barrel and hard trigger, and it's lucky to keep a 5" group at 100 yards anyway. But at 50 feet, that parallax error is something to watch out for. You can still shoot tight groups, but you have to keep your eyeball in the same position behind the scope for every shot.
The best scope I have on any .22 is a 20-year old Bushnell, fixed 4X, 30mm lens, and it sold for $25 at Wal-Mart. It has only a slight parallax error, it focuses at any distance I'd ever use it at, it's bright enough for indoor ranges and shooting in the woods on cloudy days.
I much prefer the simplicity and ruggedness of a fixed 4x scope. I don't need any more magnification than that for shooting minute-of angle. And until I get a better gun and a benchrest, I don't need to worry about hitting an aspirin tablet at 50 yards. I shoot golf balls at that distance, though.
If you only want to put a magnifying rifle scope on this gun, your best bet on rings would be the kind that will screw directly to the mounting holes in the top of your gun's receiver. Fewer layers of hardware in your mounting system means fewer things to get loose or out of alignment.
But if you might want to put a red dot scope on it one day, or some quick-detachable "back up iron sights" that many military carbines have these days, you'll want to buy a scope base that has a Weaver style rail. Not one with just two slots, which is old fashioned and only suitable for traditional rifle scopes. You'll want a base that has several slots running the whole length of the base.
The 3/8" dovetail mount that the Ruger 10/22 comes with is not a very good system. Real scopes and mounts don't use the tiny 3/8" dovetail groove. But if you wanted to buy a cheap $20 scope made for pellet guns and .22 rifles that comes with rings already mounted on it, those kind of scope rings are usually made for the 3/8 inch dovetail groove.