The mount is going to depend on several factors - diameter of scope tube, height of scope mount desired, etc., so hard to point out a single one.
I happened to use an ADM (American Defense Mfg) mount on the scope I sighted in yesterday - not mentioning the particular mount here as it came with a high end thermal scope I recently got, which is probably not what you're looking for (but I can now rule my neighborhood as I also just got in the Ruger Integrally Suppressed Barrel (ISB) fore end
). ADM and LaRue both make extremely repeatable cam lock scope mounts - I've done testing with swapping out of scopes in both an ADM and a LaRue every 3 shots and kept 30 rounds inside of 1" at 100 yards after 10 swaps. This was with a rifle that could hold 1/3MOA, so the mounts were repeatable enough to where I feel confident with them now.
So - back to the subject at hand - the ADM or LaRue (or - insert your favorite brand here, but I'm personally confident in the two I've mentioned) are if you want to be able to quickly swap optics reliably. As I also have a red dot in a QD mount for this 10/22, I want to be able to swap back and forth without having to worry about rezeroing each time. I was going to recommend a particular LaRue mount if it fit your needs, but I see the introductory price is no longer offered so you're now looking in the $200+ range. So look over ADM and LaRue mounts to see if they fit your needs - most will sit a typical scope more at an AR height, which may be higher than you want for a 10/22 - the take-down I'm using my thermal on has the stock that matches the ISB fore end, so it has replaceable cheekpieces to adjust the comb height if need be. If I were trying to mount a scope at a lower height, I'd look at the individual ring setups - any number of reputable companies make good ones. Consistent torquing of cross-bolt rings will also give you exceptional repeatability if there's not a cam lock option - I keep a torque wrench in my drag bag with my precision bolt guns for use with my Badger Ordnance rings and don't have a problem there.
Hope that non-answer helps you - I'd have to know your stock, your desired scope dimensions (tube diameter, objective lens diameter, eye relief, etc.) to give a specific recommendation. Would be happy to help there - either post here or email me.
A good takeaway going back to my previous post is I was happy with the EGW base as it readily accepts Picatinny-style mounts, which opens up the use of any Picatinny or Weaver interfacing rings/mounts. With previous factory Ruger 10/22s over the years the bases available wouldn't do that (as Picatinny wasn't defined yet) - the slots were too narrow, the dovetail was too shallow, etc.