First the gun. The caliber of the gun depends on what you intend to use it for and how you intend to use it. If it is for concealed carry defense, then the smallest guns with the power to defend you are in 9mm Luger or .380. The 9mm has more power but the .380 has less recoil. The recoil of a 9mm isn't very much but a very small gun will make it seem worse. They make small guns in .32ACP, .25 cal and .22, but I wouldn't want my life depending on one of these calibers stopping a large man.
Don't buy a real cheap automatic because you can't afford a jam in a carry gun. If you are going to use the gun in your home for defense, then a larger gun is easier to handle and has less felt recoil. A 9mm is a good choice for this but .40 calibers and .45 ACP are also popular calibers. Don't totally discount a revolver for home defense as these are simpler to use and are more reliable if you never take it out and clean it. If you keep it clean, modern autos are very reliable.
As for safety courses, the NRA has pistol safety courses. Just google NRA and your zipcode. Some states require a permit to carry concealed and some do not. Some states even require a permit to just possess a pistol in your home. A pistol is a poor choice for defense, however, unless you are willing to practice with it. It is real easy to miss when your full of adrenalin and scared. You ahve to practice. A shotgun is easier to hit a target with, but cannot be easily concealed. Notice that when police (who have been trained with a pistol and who (hopefully) practice are expecting trouble, they grab the shotgun.
Popular brands of small automatics are Glock, Sig sauer, and beretta. People will augue about which is best but I suggest holding each (and if possible, have someone let you shoot one) and seeing which feals best in your hand.