Pre-stretched canvas is convenient, because it's already stretched and put onto stretcher bars for you. If you're just getting started, this is definately the way to go.
However, pre-stretched tends to be not stretched as well, and usually comes with thinner cheaper canvas, and often has too much gesso on it... the edges are gessoed over as well (because of the mass produced sheets all being covered in gesso), which may be fine--but is limiting because it may not be what you want. Many people prefer keeping the raw canvas or linen on the edges of their canvas.
If you stretch your own, you can stretch it tighter (or looser, if you prefer), though this takes some practice. You can also paint on exactly what surface you prefer to paint on: more or less gesso, sanded to your liking, oil vs water based gesso, etc. The canvas itself you may also choose to be any one of a variety of materials. The size of the canvas may also be specified exactly as you prefer, and the stretcher bars may be of any thickness you choose, etc. Options options options.
These options are things that you naturally will come to explore, as you gain experience. There's nothing wrong with starting out on pre-stretched canvas, if you want to get started with painting right away. Eventually though, it's a good idea to learn the art of stretching and preparing your own canvas. It makes a difference not only in the experience of applying paint, but in the appearance of your final piece. There are many options available when you stretch your own canvas, and that's the main point. It's easier to learn how to stretch canvas from somebody who knows how, but it's also perfectly possible to find some good instructions (possibly from a book) and do it that way.
Once you've become familiar with this stuff, you might consider paying other individuals or companies to stretch canvas for you, to your exact specifications. This isn't something you'll want to do until after you've gained enough experience to know exactly what you want. It's very common however--many (possibly even most?) experienced painters do this.
On canvas, the 2 most commonly selected options are oils and acrylics, though there are many other possibilities to choose from. Some suggest starting out with acrylics, but I don't agree. I think it's up to you, and it completely depends on what you're trying to do. You should definately talk to somebody at the art store about this. Also, be sure to tell them that you are somewhat new to painting, and would like recommendations on all of the other materials you'll need to get started.
Acrylics are cheaper and dry faster, but oils are more flexible for certain things. For one, it's much easier to paint "wet on wet", meaning that when you paint, the paint "blends" into the paint underneath (the "ground" or "background") more readily, because the background is still wet. This is difficult with acrylics because it dries so quickly. Chemically, the two are very different, and this produces subtle differences in color and texture that are hard to describe.
You'll really just have to experiment with both--in fact, i'd recommend getting a small starter set of each if you can afford it. Otherwise, talk it over with the people at the art store; most art store employees are more than willing to share their knowledge with a beginning painter.