How can I photograph printed design work on a budget for a clean portfolio look?

BobT's answer is what you want if your aim is document copying. I have to assume that what you want is something different: a pleasing presentation of a physical artifact. A "product shot" of the printed material, if you will. (For those who haven't been paying attention to the design world, it's kind of a vogue at the moment). Otherwise you'd just export your work as a JPEG or PNG in sRGB and be done with it, right?

Your basic thinking is right on the money, and you don't need a lot to accomplish it. You'll need a light source with decent colour performance, a tripod (assuming that you won't be using flash as your light source) and a camera that's capable of either producing a RAW file or fine, wide-ranging adjustment of colour temperature (not just a tungsten/daylight/shade menu).

The light doesn't need to be anything special, as long as it's adjustable and somewhat controllable. An Anglepoise-style desk lamp would do perfectly, as would a clamp-and-reflector worklight if you have something to clamp it to that would allow you to adjust its height and direction. Either tungsten (old-fashioned is okay, but high-temp or halogen would be better) or a compact fluorescent with a high CRI will do. As long as there's a shade or reflector of some sort that will allow you to control where the light is falling, you'll be fine. Ideally, you'd want the printed matter to be in a sort of pool of light (particularly with darker card and identity designs). Use the position and direction of the light source to control where the shadows fall, and perhaps to pick up the edges of the paper or card stock. The fill from the reflector will keep the lighting more even across the printed work, making sure that nothing is actually obscured. (The viewer's eye can adjust for minor variations if the lighting is simple and understandable at a glance.)

Keep an eye out for glare from the stock; even the sizing on bond or uncoated card stock is pretty reflective. You can use that to your advantage with a raking (lower-angle) light if the texture of the stock is important.

Since your light is likely to be relatively low-powered (from a photographic perspective; it may seem bright to the naked eye), you're probably going to be working with a shutter speed that makes hand-holding the camera impractical for a shot that needs at least some crisp detail. A tripod, or some other way to fix the camera in space, will almost certainly be necessary. If you can avoid touching the camera at all during the exposure by using a self-timer, remote control or cable release, that would be even better. So you're set to go there.

That leaves the colour of the image. You'll want to have a decent level of control there, which is why a RAW file is the better option. Since you have a T2i, you're coveredd in that department as well. You'll have the RGB (or CMYK) values of the original work handy, of course, but Pantone-perfect colour matching might not be exactly what you want. You want something that is perceptually the same, given the context in which the image is read. That may mean that the mid-lit (neither "in the spotlight" nor in the shadow) areas of the product are an art director's dream match, or it may mean a slightly warmer or cooler rendition. It really depends on the context you're building in the overall image; you may want to go a bit warmer for the desktop scenario (especially if you're doing, say, letterpress on a softer, handmade or mouldmade stock or laid paper), or a little cooler for something meant to seem a little bit "techie". It's hard (but not impossible) to get that level of control in camera, but pretty easy in, say, Adobe Camera Raw (which you'll have if you use Photoshop) or in your camera's included software.

As for the lens, you'll probably find that the el-cheapo 18-55 is probably the best of your current kit for the task (though the 17-40 might be better once you get it). Long is not necessarily good for what you're doing, since it will give an odd perspective to anything that isn't shot dead-on flat. Most of the range of the 70-200, for instance, will give any oblique-angle shots a sort of isometric appearance because the far side of the object isn't proportionally far enough away from the camera compared to the near side. Even the "nifty fifty" might be a little long for larger stock like letterhead (although it would be tremendously useful if you wanted just a narrow strip of a business card in focus).

So, to sum up: a light that you can position and aim, and you're good to go.