Of the two cartridges you listed, I would choose the 243 hands down. If you're not dead set on getting a 243 or 30-30, though, you should really take a look at the 7mm-08. It'll handle everything from coyotes to elk with minimal recoil and great performance.

If you're young and still not big enough to comfortably handle a full-size rifle, you ought to take a look at youth rifles, such as the Remington Model 7 Youth.

One more thing- if you've never shot a scoped gun before, ask your dad if he can put a scope on one of your .22's, then practice with that .22 as much as you can. Pretend like you're shooting a big game rifle. Take your time on every shot and practice controlling your breating and squeezing that trigger nice and smooth. Then, after you've gotten in a lot of practice with your .22, move up to your big-game rifle.