This is probably the most important thing you'll need to know as you play Final Fantasy VII. While you should have a working knowledge of materia from the game manual (you did read it, didn't you?), it doesn't tell you many of the finer points of materia raising.
First of all, always be aware of who is holding what materia. I know it sounds hard, especially farther into the game when you've got a truckload of the stuff, but a simple exercise in forethought can clear up this problem. Any time you change a character, change their materia as well. For instance, if you want to take Aeris out of the active party and replace her with Barret, go to the Exchange Materia menu and give Barret all of Aeris' materia. The way I like to do it is I keep a specific group of materia with the active party at all times--leaving the rest unequipped--until they gain the desired level. As soon as this happens, those materias are replaced with the next ones I want to gain a level or two.
Second, use the double and especially triple AP weapons and armor as much as humanly possible. Sure, after a while they seem pretty weak as more weapons and armor become available to you, but unless you're going to fight a really tough boss, why not give Cloud the Apocolypse instead of the Ultima Sword? The benefits to your materia in the long run greatly outweighs the extra damage you'd deal during battle with a better weapon. Actually, I have been known to use my double-AP weapons all the way until the beginning of Disc 2, and my triple-AP weapons for most of Disc 3. Double-AP armor should be used whenever possible.
So what materias benefit most from gaining levels? Well, unless you're trying for the Master Materias later in the game (see the individual materia sections), you should get all the spells from your Green materias, and then de-quip them, only using them therafter when you need their spells. Most Blue and Purple materias don't really benefit much from gaining levels, although Purple ones do tend to benefit more. For instance, HP Plus increases your HP more as it goes up in level--definitely reason to keep a few of them in your high-yield materia slots! As for Yellow materias, only a few of them actually increase their powers with an additional level. However, if you want to get at least one Master Materia and don't want to try too hard, equip all your Yellows and go for Master Command, as Yellow materias generally have only two or three levels to attain, whereas Green and Red materias have four or five!
Oh yeah, and of course, when you do get a materia to Master level, it will replicate itself, making a new one that starts at level 1. While this may sound pretty cool, note that a good many materias can be bought if you want another one, if you actually want another one at all. I have yet to find use for a second Choco/Mog.