Almost anything will work on a .22 except for scopes with 100 yard parallax settings (centerfire).
I like the following:
Simmons WTC, this has lots of magnification, really good glass for a $99 scope, and an adjustable objective. It is big though and heavy, this will fill the target shooting role very well on a budget.
The other is the Nikon Prostaff 4x. This is a fixed 4x, parallax is fixed at 50 yards. This has excellent glass for the money - perhaps the best in this price range, and being a fixed power, not a variable, the image is very crisp. It is $99 at Wal-Mart. This is the best all-purpose rimfire scope. It is light, handy, and high quality. Can shoot targets, hunt...does it all.
I wouldn't spend more than $100 on a scope for a .22 unless you are a very serious competitor. I've shot tons of 1-hole groups with the Simmons, and no scope is going to make those groups any smaller at 25y or 50y.
Consider getting the Weaver TO-9 rail for the 10/22 ($9). It replaces the cheesy 3/8" scope rail with a full size Weaver rail with grooves. This lets you use real 1" rings, and these will not move or shift.