No, it doesn't have to be specifically for rimfire.
One reason you see certain models called out as "rimfire" is that they are not made to hold up to the greater recoil of larger caliber rifles. The only reason I would suggest a rimfire scope is that they are usually much less expensive. The Simmons 3x9 I put on my .22 was only $30.
As far as sighting a scope, it's not all that hard. There should be plenty of on-line how to videos out there...