Luepold makes some great rimfire scopes. Since this is a heavy barrel gun I would suggest the 3-9x33mm EFR rim fire,it has adj focus from say 10m to infinity. Its has the fine dupellex reticale to.

I have the standard 3-9x33m EFR on a hornet and a 3-9x33mm light weight with fine dupellex and parallex set to 60 yrads as most RF's scopes do. This is on a 22WMR and it works great. I also have the 2-7x28 RF on a 22lr but would prefer the 3-9x33 on it to. I sent it to Leupold to have the retical and parllex changed.

These would run from $200-$350 but are the smallest and best scopes for a 22lr.