I'm using a Canon T1i (so is Brie). I've used the kit lens for quite a while which is a nice lens, but won't give you "true" macro. I recently picked up a Canon EF 100mm f/2.8 Macro USM, which is a true macro lens, but is also quite pricey.
It really comes down to how much money you're comfortable spending and whether or not "true" macrophotography is what you're after, which you probably aren't. True macro requires a lens with a magnification ratio of 1:1, meaning an object that is, say, 1/4 inch wide will form an image on the sensor that is 1/4 inch wide. Most lenses are more along the lines of 1:4 or 1:3, as far as I know.
If you just want "closeup" photos (which a lot of people call macro photos), a lot of PnS (Point n' Shoot) cameras will do you just fine for between $200-$400, depending on how nice a camera you want. If you really want extreme closeup, get a PnS and a few lens adapters, like mass has. That'll give you great results, as his example demonstrates. And probably one of the better "bangs for your buck."
If you really want a DSLR (one of the fancier ones, not a PnS; although they do have a full auto mode - largely a waste of money to buy a DSLR and use full auto, though...), you can go ahead and get one and simply use magnification filters such as
these (which you can see are quite inexpensive), and they will often give you some nice magnification ratios at the cost of image quality. Most if not all of those will give you pretty bad distortion everywhere but the exact center of the image, kind of a fisheye effect.
Yet another option, if you do want a DSLR, is to just use the kit lens with an extension tube. An extension tube is pretty straight-forward, it's just a tube that goes between the lens and the body, allowing you to get your lens closer to the subject while maintaining focus. This is an excellent option, and again pretty cheap, like
this set. The drawback of these is that you'll be required to have much longer exposures. Also, unless you get a more expensive, nicer set, you also lose autofocus and aperture control. Tubes can be stacked, as well, to get you extremely close to the subject.
Tubes and filters can also be used in combination. That's a good bit of versatility for $20.
I do have to highly recommend a DSLR, just because I recently made the switch (... like... a year ago? Something like that) and never looked back. The amount of control is incredible, and image quality is definitely noticeable. Just keep in mind, if you've never used a DSLR (which I hadn't), it can be a pretty steep learning curve. But photography, even on the amateur level, can really be a blast, which is why I recommend a DSLR. Gets you more... "into" your pictures, more invested.
Whatever you do, good luck. Macro and closeup photography is probably my favorite. It allows you to see so much that you just wouldn't be able to with the naked eye.
Hope all that helped some. O_O
EDIT: Figure I should mention one last thing. I can't recommend Canon highly enough. I don't have a ton of experience with cameras, but the few I've extensively used have been Canons and they're wonderful, wonderful cameras. And if you get a Canon PnS, there's a good chance you can use
CHDK, which is a firmware hack for Canons PnSs that will give you a ton of extra control over your camera.