If you are between the age of 18 and 21, go with a .22 semi-auto rifle or carbine. The two most common and best are the Ruger 10/22 and the Marlin Model 60, I believe it's called. Both are rather inexpensive, reliable, have no recoil, are accurate and the ammo is super cheap. Learn with that and work your way up as you improve.
As for .22 caliber handguns, they too are the best place to start. But you do have to be 21 to legally purchase a handgun. I'd prefer starting a new shooter on a revolver (preferably 4" barrel as it's a good combo for accuracy and balance). For semi-autos, I like the Ruger and Browning Buckmark.
If you are serious about learning about firearms, that's the best advice I can give you. And get someone who really knows what they are doing to teach you how to use them as well as gun safety. Learning the safety aspects is the most important part of it all.
-CH