Magic Users are many things to many people. Here is how I handle them, for what I perceive as highest in-game enjoyment by players, as well as most theoretical consistency within the campaign framework.
The world is full of magical power and magical creatures. Humans, however, are considered mundane creatures, not magical by nature. Thus, human magic users are not themselves magical, they simply learn the correct methods of harnessing the magic power of the natural world.
Magic Users are like scientists, who use formulas to tap into the power of that magic world. These formulaic methods involve especially the use of magical chemistry, harnessing the magical energy in magical creatures and objects. Another important method involves magical power words, and a third method involves magical symbols. Through magical ingredients, magical power words, and magical symbols, magic users release and channel magical power.
I reject the mechanism of "memorize, fire, and forget". Not only does it render our magic users drastically underpowered, it conflicts with our general cultural expectation of how magic works, as defined by such characters as Harry Potter. The hard part of D&D magic is that there is NO popular culture depictions of magic that function that way. And frankly, it is a bit lame to any young person who wants to play a magic user, based on their enjoyment of Harry Potter, for example, to discover they can only use one spell a day.
In slightly reformulating the magic user mechanic, we can build on the basic logic of D&D magic. As Gygax says, the power of the magic does not come from within the magician, he is just a conduit. However, the act of casting and being a conduit for the energy does take a toll on the wizard's own energy level.
Thus, rather then the spell slot structure, we can postulate that the natural limit to a wizard's spell casting is his constitution score. Think of it like this: a pipe can pass a powerful jet of water through it, but the pipe itself can only take so much pressure before it breaks. A thin pipe can only handle so much pressure, while a thicker pipe can handle more. If the magic user is the pipe conduit, his CON measures the thickness of those pipe walls.
The end result is similar to traditional 1e limitations, in that a magic user has only a certain number of spells he can cast per day, and he must get restful sleep before he can regain more spells. However, now he has more spells to cast, at least at the lower level, rendering the magic user more useful on an adventure, more able to use magic, and therefore, more fun to play. A higher level magic user would be punished by the CON limit, but he overcomes this natural limit on spell casting by becoming an expert in channeling the magic through other objects, such as scrolls, potions, wands, staffs, etc.
In game play, for fun and ease of play, a magic user can fire off his spells more or less instantly, needing only as much time as it takes to say the power words, draw the symbols, or employ the material components. Thus, a magic user is prevented from wearing armor, because he needs easy access to his material components (in the many pockets and folds of his robe, hat, boots, etc) and ability to smoothly and unerringly weave symbols in the air, on his body, or on the ground.
Magic in Other Races
Humans are the only race that can become powerful magic users, because the other races are themselves magical creatures. In other words, elves are not just thin humans with pointed ears who live in forests. There is a qualitative difference, because Elves are a magical race. Likewise, Halflings, Dwarves, and Gnomes are not just midget humans, they are magical races of their own, with their own special dweomer.
Magic use by humans is a form of technology, and humans developed the scientific knowledge of magic because they are otherwise non-magical. Thus, the other races have racial limitations on their advancement as magic users. The origin and practice of human magic is alien to them, and they can never truly master it's usage. The case is much like humans and silent movement. With much training and practice, humans can learn to move silently with more and more skill, but they will never attain the native mastery of the elven race.
The closest thing approaching a "naturally magical human" occurs in the case of psionics. Psionically endowed people attain powers that are similar to magic, but they are inborn, not dependent upon power words, symbols, or magical ingredients. Thus, psionic powers appear to be more related to divine power than magical power, and are probably a vestige of the divine lineage of some human families.