You dont need to break the bank, some seekins/vortex precision rings will do exceptionally fine and if you are going to spend badger money I would go ARC M10s first. Bottom level I would be comfortable with for precision would be the burris with the inserts.
Hell, I have some of the bottom level vortex rings that are 20 buck a piece for my 22, im not 100% confident its its ability to hold up to abuse on something reasonably large but for my big ass 22 they work fine.
For your AR (presuming full picatinny up top) go with 1.4-1.5 in height so that you can get your eye behind the scope without distorting your face.
I also agree, so long as your scope has over 50 moa of travel a 20 moa canted base wont hurt.