Picatinney style. . . .or maybe a quality Weaver style? Steel or quality aluminum picatinney base and rings will mount much more solidly. They stay tight because they hold torque. Almost all cheaper rings and bases won't hold torque in my experience. They hold torque because the force is spread out over a larger area and the individual pieces are stronger. The cheap thin stuff, IME, just bends until all or most all torque is lost.

Quality brands I've used are TPS and Larue Tactical. There are many other good base and ring suppliers. Ferrell, Badger and others come to mind. I think I would be willing to try Leupold PRW's on a good TPS or similar 1 pc base for a lower cost base and rings. A friends rifle has Burris XTR rings on a Millett base. The cross bolt's nuts are kind of eating the rings, but they still hold torque. I think a previous owner over torqued, guessing at how tight they should be.

A decent 1/4" torque wrench will give you some help getting in the torque range you need.