I would replace the scope base with a Weaver TO-9, add Burris signature rings and top it with a 3-9 or 4-12 scope. I' d make sure the scope is Adjustable Objective(AO). That means that you adjust the focus based on the distance you will be shooting to make sure both the target and the crosshairs are in focus.
If you want to go cheaper, there are scopes that are made for rimfires that have an objective set for like 50 yards. The Simmons 22Mag is one, I think.
You can also replace the bolt stop (steel) with a polymer buffer. That will (IMHO) reduce the small recoil that the 10/22 has and keep you on target for follow-up shots.
Brian.
Check out www.rimfirecentral.com for a ton of info on the 10/22.