Warne Rings are good rings for the Remington with 3/8 Receiver Grooves. They also have the 22 scope rings for a 1" scope. I am partial to 1" Tube Scopes for the 22 Rifle. You can just see so much clearly vs. the smaller 22 scopes.
I would say you probably want them in Medium Height. You can find them and their products on the Internet.