Without a doubt I will recommend a Simmons .22 Mag scope. That's what it's called. Straight 4X. I have two on some of my Ruger 10/22's and my brother has one on his 10/22.
TONS of rounds thru these things and never a problem. Plenty large objective dia for a .22 and I feel the Simmons .22 Mag offers superb clarity.

Choose a finish of Matte Silver (#511033)MatteBlack (511022 or Gloss Black (511070). About $50 new, but I wouldn't really hesitate to shop ebay. My brother got his there for under $20 with a nice set of ringsand 2 factory 10/22 rotary mags. It works great.
Simmons offer these invariable power (3-9X) but (IMO) I can't see how that would be necessary unless it's competition.

