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Burris Z rings are popular.
I have 3 sets and they have been great. I've had others that were good also.
Recoil on the 10/22 wont be much for the set up, but why cheap out? You may want to use them on something different later, so buy decent ones, once.
I just cheaped out and bought tasco rimfire mounts for 8$. Big mistake. Spend a little more for some decent rings,I think I will go with the Burris or Weaver steel rings next time.