The grip on your racquet is almost as important as the strings. Too small a grip and you'll forever be worrying about blisters and the racquet spinning in your hand on mis-hits. Too big a grip and you can worry about tennis elbow and hand and wrist fatigue.
So how do you know the right grip size? Easy, just grab the racquet like you're shaking hands with the grip and the pad of your thumb should sit right on top of the nail on your index finger.
You can use overgrips or not, spongy grips or hard leather grips. It doesn't matter, as long as it's comfortable.
As for how to hold the racquet . . . that's up to you, too!
It used to be that beginners were taught with an Eastern Forehand Grip, where the "V" between the thumb and index finger on the playing hand was right on top of the racquet. That's the way I was taught and that's the way I would teach a beginner. The Eastern Grip is the most versatile of all grips. The palm is right behind the racquet. The Eastern Backhand Grip is simply shifting the V to the left bevel of the racquet (for a right-hander).
Other grips are the Continental (which I use and don't recommend) the Semi-Western and Full Western. The Continental is close to an Eastern Backhand Grip while the two Western Grips make the player move his hand a long way to get a good backhand grip.
The reason I don't like the Continental is it is a grasscourt grip, good for chip forehands, low balls and net rushers. It's tough to return high balls with this grip and promotes wristiness. I get away with it, but wish I had an Eastern Grip.
The Semi-Western Grip is very popular and is acheived by putting the flat part of the thumb (between the two knuckles) on top of the racquet. This grip allows for ample topspin, but isn't great for volleying with. Most women pros use this grip, a good mix between power and spin.
The Full Western Grip puts the thumbnail itself on top of the racquet and the palm underneath and produces wicked topspin. I still haven't figured out how anybody can hit with this grip, but all the Spanish and South American clay court specialists must know something I don't because it works. Just watch Nadal play to see a Western Grip in action. You need to swing very hard to hit a Western forehand.