what rings should I buy for the Savage Arms Mark-II BV?

Probably medium but as gunsasauras suggested bring the gun along. I have BKL 257 rings on several of my guns and really like them. High quality alluminum ring for 11mm or 3/8 dovetail and relateively inexpensive.
 
your savage should have the weaver bases installed on the reciever and not the dovetail, you can use a set of medium weaver bases if you don't have the adjustable objective but if your scope is a AO model chanses are you will want the high rings for clearance on the bell. The BKL rings fit the standard 3/8 dovetail but most savages are drilled and tapped with the standard weaver bases installed. If it is drilled and tapped with no bases you can use two weaver number 2 bases, then regular weaver style rings.
 
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