You have received pretty good advice in all responses...If I could add something it would be about no over-torquing screws...Target for 40 in./lb. to a max of 45 in./lb...Most modern rings are good quality, with CNC machining the tolerances have narrowed favorably.
BKL, Talley, Warne, and many others are about in the same league (very good rings) and are cheap...don't mix or reverse the upper halves (of the rings) because some manufacturers have machined and lapped them as they are in the package.
I center the scope turrets by counting the clicks end to end and going to the middle, and always lap the bottom halves of the rings once they are mounted on the gun (to seat the scope perfectly)..,I use laping bars and 320 grit lapping compound.
Optically centering the reticle of a scope works fine but in a good scope counting clicks and going to the middle does pretty much the same job and it is easier and faster to do...
If your gun has the grooves cut straight and you get any of these good rings you shouldn't have any problems requiring windage shimming. When you do need it, it is usually a misaligned groove, a no well seated ring or defective ring...Scopes of good quality very seldom are the cause.
If your scope is out of range for elevation, then before anything else check the barrel...I have seen many barrels off center (pointing up or down)...I usually try to straighten the barrel first and/or machine a bushing and center the bore/ barrel, but other people rotate (index) the barrel around the receiver...I don't like indexing, the barrels are either perfectly straight and centered or they are not part of my gun...To me indexing a barrel is like starting a F1 race with a patched tire.
Hope my $1 contribution makes sense and helps you with your project...
Last edited by azuaro; 18th January 2016 at 10:44 PM.