To put a scope on a Model 61, you need to install bases first. The gun will need to be drilled and tapped to install the bases. You can use a Weaver #2 side mount base or for top mount, a round barrel version takes a #19 and a #13. The octagon barrel version takes a #25 and a #32. For the side mount, you will also need a side mount which includes the rings. For the top mount you will need rings and then any 1" scope that you want to use.
You can purchase the bases and rings at Brownells and any gunsmith can drill and tap your gun.
I hope this helps you,
You have one of the later guns, early ones did not have the grooved receiver. I like the Millet windage adjustable rings. You can adjust the scope for windage with the rings instead of using up all of the scope adjustments. The following rings will fit your gun.
A 3 x 9 x 40 scope is all you will need for a 22. The Bushnell Banner is a good scope for the money and has a lifetime warranty.