Jim,
If your rifle is shooting that well you are good to get into this game. In reality what most guys do not realize is that the scope is the thing that needs upgrading more times than the rifle when someone is starting out. An excellent rule of thumb is that the scope and mounts will cost at least as much as the rifle. To really enjoy the potential of your rifle you will need a scope with accurate, reliable, repeatable turrets - power can be from 10-15 power, you do not need more. As you get into this you will become aware of how important the turrets are, then you can decide on the reticle, then on what paralax adjustments (side turret or objective), then on a mounting system that incorporates additional elevation. You can go the Chevy route or the Cadilac route with optics - suggest you stay away from the real low end stuff because you will end up buying good stuff eventually.
Best advice I can give you is to find a suitable safe practice location, find a partner, get some targets, get some knowledge, shoot in windy conditions as much as possible, keep diligent notes and be prepared to load a lot of ammo. Hitting steel plates at 700-1000 yards is how we practice for our hunting seasons, my plates range from 6"x6" up to 2'x4'. Bottom line is to learn from your shooting, then skill will develope, then confidence will develope, then critters will die way out there.
Go through the FAQ and the search function and you will find a lot of basic info here to get you going. Ask questions, that is how most of us got into the game. Get your skills up to the potential of your equipment, then upgrade your rifle - by the time you are really getting into the long range game that .300 will need a rebuild.