You can check with your local gun stores about places to take classes or receive training, even the people at a place like Bass Pro will probably be able to point you in the right direction. Heck, even the people at Wal-Mart might be able to help, but I wouldn't go there first haha. Google can also work wonders, just search for your state and "gun classes" or "hunter safety" and you'll be on your way.
Personally I would suggest getting a shotgun as your first gun, it is a lot of fun going to the range and shooting targets but nothing really beats taking a buddy out with you and spending the afternoon shooting clay pidgeons. Moving targets are much more fun, and make you a better marksman IMO. I wouldn't suggest buying a 12 gauge, those guns are heavy and have more kick than a smaller gun. I would suggest a 20 gauge shotgun, it's much lighter and easier to handle (plus it's easier on your shoulder!) and if all you're doing is shooting clays it provides PLENTY of power haha. Anything you want to hunt with a shotgun can also easily be taken with a 20 gauge as well, except maybe a turkey. Even then, shoot it in the right place and you get the same result. Most people would suggest a 12 gauge because POWER! SIZE! MORE! but I think if you really view a gun as a tool you should select the right one for the right job. Just like you wouldn't use a giant power sander or saw to make a pinewood derby car I feel a big, heavy 12 gauge is overkill for the kind of shooting you seem to be looking to do.
If you want a rifle, go with a .22 because ammo is CHEAP and you can have a lot of fun plinking targets with a gun that has no recoil and many of the same features as a much more expensive rifle. As you get more accustomed to guns and the hobby you'll probably want something more powerful, but as far as target practice and taking small game goes nothing really beats the price and ease of a .22.
Pistols... I don't know much about. I know you can hunt with one (but personally I'd rather use a rifle or shotgun) and they are a TON of fun to shoot at the range, but to me a pistol is more of a self-defense weapon. For someone who currently doesn't own a gun or have much experience, I feel that a rifle or especially a shotgun will provide you with a much more fun shooting experience. Besides, if your mom's boyfriend owns a few pistols you could just go shooting with him, it'd be much cheaper than buying your own and you could still get a feel for the gun all while having a nice time with him as well. Win-win, IMO.