presuming your rifle's receiver has scope base mounting holes that are properly aligned, then you should have little trouble mounting a scope to properly align with the bore.
Many shooters prefer the Kelbly/Stolle dovetail, Weaver, and Picatinny types of bases, as they don't require any twisting or turning of the rings like the Redfield type bases.
Another thing to try might be to mount your base and rings, and then put a long straight piece of PVC pipe or wooden dowel in your rings and see how closely it follows the barrel.
Lastly, don't think you need to have the scope perfectly aligned, so that you won't have to make a single windage adjustment. That's just not practical, and scopes have windage adjustments for a reason. You'll want your scope pretty well centered of course, but don't go crazy with this stuff.
Greetings from Canada, Its cold outside. Sako/Tika make mounts with a Plastic/nylon insert which takes the stress of the scope. These inserts work as a swival in the mount and will not allow any movement from the largest mag. shells. Burris has a similar set of mounts which work just Excellent on all weaver type mounts. Burris also have optional ring inserts which can be purchased in 5, 10 & 20 1000's" this will allow the shooter to shim a badly aligned base or just shim for those extra long shoots. I own both Tika & Burris both are great. Hope this helps