This really depends on your photographic goals. Here are some possibilities to consider.

But before you rush out and buy a lens based on these suggestions I strongly recommend trying out the lenses you’re interested in before you buy. Most decent stores won’t mind if you go in with your camera and roll of film or an empty memory card and take a few shots of the shop using a couple of lenses. (be sure to use a tripod or rest the camera on a sturdy surface and use identical settings for each lens) They might grumble a bit, but how else can you decide whether a given lens is good for you? Certainly you don’t want to be trusting the advice of random people on the Internet!

Cheap prime lens.

If your primary objective is to learn more about basic photography skills and take photos of reasonable quality then your first lens should probably be a Canon 50mm 1.8 lens. This is a very fast fixed focal length lens. But since it’s technically easy to build a 50mm lens, it’s also astoundingly cheap. New Canon 50mm 1.8 mark II lenses can be bought for as little as $75 US.

Such a lens, while cheap, takes sharp clear photos and can be used in extremely dim environments without the harsh light of a flash because it’s so fast. So the photos you take with it will look better than those from a typical point and shoot both because they’re sharp and because you’re not bathing your photos in ugly glaring light from a camera’s built-in flash. Natural light photographs almost always look better than on-camera flash.

Of course, since it’s a prime lens you will have to walk around more to get a lot of shots framed right. And some wide-angle or telephoto-type shots you won’t be able to get at all, so those are the obvious disadvantages.

Note that Canon have made two versions of the 50mm 1.8 lens. The older lens has no Roman numeral designation and has a metal mount, a distance scale and an optional clip-on hood. The mark II version has a plastic mount, no distance scale and a clumsy screw-on optional hood. If you can find an original lens it’s probably worth going for - it costs as much used as the mark II does new, but is of slightly tougher build quality. Optically the two lenses are basically identical. Canon also sell the 50mm 1.4 USM, which is optically a bit faster and uses a USM drive with FTM, but it costs considerably more than the 50mm 1.8.

However, if you use a digital camera with a cropped sensor (basically any EOS digital camera except for a few top models) then the 50mm might be a less useful choice, since it essentially behaves like a longer telephoto on such models, and won’t let you get in much of a scene. In such cases a 28mm 2.8 might be a better option.

Cheap zoom lens.
If you value convenience and image quality is not a priority then an inexpensive zoom lens, such as the kit lenses sold with consumer-level cameras, is fine. However I don’t recommend most of these lenses (the “cheapies” in category 1 above) to anyone who’s at all interested in photographic image quality. The one exception is probably the EF-S 18-55 kit lens included with the EOS 300/350/400 and Digital Rebel series cameras. This lens, while incredibly cheap, is actually not too bad if you factor in the low cost. Especially if you stop down to f/8 or so when using it.

So what if you’re on a budget but really want the convenience of a zoom? Well, you could pick up a used zoom lens of an older generation, many of which have quite decent optics for the price. For example, you could buy a used metal lens mount 28-70 3.5-4.5 II for nearly the same price as a new 28-80 all-plastic cheapie. If you want a lens with silent-focussing USM you could consider the metal lens mount 28-80 3.5-5.6 USM (not one of the later plastic lens mount models with Roman numerals), which has similar build quality to the 28-105 3.5-4.5 USM. Two other reasonable but discontinued lenses available inexpensively on the used market include the 35-135 4.0-5.6 USM and the older 35-105 3.5-4.5. The main drawback is that these lenses aren’t really wide enough to be useful on cropped digital SLRs.

In short, you don’t have to put up with shopping mall quality just because you’re on a tight budget so long as you’re willing to consider used lenses.

Mid-priced zoom lens.
If you have a slightly larger budget, a mid-priced zoom (category 2) is worth considering. For example, two popular Canon zoom lenses are the 28-105 3.5-4.5 USM and the 24-85 3.5-4.5 USM. Both are reasonably sturdy lenses with decent though not outstanding optical quality. They feature fast and silent ring USM autofocus motors. They’re more expensive and heavier than cheap zooms, but most people find the tradeoff worth it.

Of the two lenses the former has a bit more reach and so is good for isolating objects or for doing simple portrait work. The latter has less reach but is considerably wider (there’s a surprisingly big difference in coverage area between a 24mm lens and a 28mm lens) and so is popular for travel photos. The 24-85 is also a good match for those digital cameras with less than full frame image sensors, such as the 300D/Digital Rebel/Kiss Digital or 10D.

If you’re interested in the 28-105 3.5-4.5 USM see the important note below about its similarly-named low-cost cousin.