What I intend to do to my stock is this: Drill a 1/4" hole where the rear screw goes into the stock and then fill it with Devcon. This will give the screw something solid to attach to.
As for your other questions: Shoot it as is. Get a baseline so that you can see the effects that later changes make. If it's not satisfactory, float the rear tang. Savage rifles seem to perform better with the tang floated. Regardless of how it shoots, I'd definitely bed the recoil lug at some point in time.