Pepaw, I use Burris Signature Zee rings almost exclusively, mediums more often than not, just depends on the scope and where ya need to position it. Sometimes due to a larger than normal power ring or ocular bell I need to use high rings, but not very often....I would recommend you remove the base that came with the rifle, clean the bottom of it real well along with the top of the barrel and the screw holes, there will probably be thread locker in the screw holes, dig it all out, I use a leather sewing awl and a bit of heat to get it out easier. Next, take a straight edge and lay it on top of the barrel lengthways and see if the mount holes have a burr on them, just about everyone of those I have checked recently will have burrs around the holes, take a fine file and remove just the burrs, you may need to touch up with a little bluing. Then take a piece of 240 grit wet/dry paper a bit bigger than the base is long and lay it on top of the barrel, place a few drops of oil on the paper then lay the base on it like you were mounting it. Hold the sand paper still and work the base forward and back carefully keeping it in the correct position on top of the barrel. What you are trying to do is lap the bottom of the mount so it fits the top of the barrel perfectly, it doesn't take much, you'll see where it removes the finish from the bottom of the aluminum base. Clean the base and barrel well and put a liberal amount of blue loctite in and around each mount hole, then mount the base. Wipe the excess loctite from around the base and make sure none went between the breech and barrel. Mount the rings and scope as usual.
Tim