We need to know a few more details about the kind of target shooting you wish to do in order to make the best recommendation. With a Savage Axis, I assume you are talking about informal target shooting. Some general comments. Your scope budget is not very large, but I think about right for a Savage Axis. To get experience, you need to shoot at 50, 100, and 200 yards at first. A 3-12X would be adequate, but a 4-16x might be tempting. Your budget will keep you with Simmons and Bushnell, primarily. Weavers on sale would also be good. They have decent, low priced scopes. The Bushnell Trophy 4-12x sells for less than $200. Mine has worked great for years. So has a Simmons Whitetail Classic 4-14X. For myself, I would avoid Barska, BSA, Tasco, and other traditionally cheap brands that are advertised everywhere, although some may report that they have had decent luck with some of these. You do not need a 50 mm objective for target shooting. That is mainly for hunters shooting game in the woods at sundown.