I own an Lee Enfield Mk I. Can't go wrong for nostalgia, simplicity, knockdown power and beauty. But .303 is fairly expensive.
First rifle, I would get a Ruger 10/22. Cheap ammo. Will kill anything with enough pulls of the trigger. And you can always upgrade it as time goes along. I''ve put a 1" bull barrel on mine, new stock and a 3x-9x variable scope. It is an absolute tack driver. And 25rd magazines are a plus. You can buy after market triggers, high capacity magazines, sights, etc.
If you can't purchase a semi-auto, a 16" barrelled Winchester lever action in .357Mag is a good choice. You can shoot .357Mag 200gr flat points for serious targets or .38Spcl for plinking. This is a REALLY compact and light rifle that is suited for outdoors as well as next to your bed.