Never had a problem with Weaver bases and mounts moving, if installed correctly. They're solid, inexpensive, and allow a person to exchange scopes easily while maintaining zero. If you go on a hunting trip, you can take a back-up scope, all zeroed, and don't have to worry about losing several days of hunting with your favorite rifle/load.
The regular-type Weaver rings, but with four screws each are the ones I prefer, just because the scope tube doesn't tend to rotate as screws are tightened.