DS > DSL > DSi
Here is how.
The original DS is cheap and only has a less bright screen, has a GBA slot, slightly bigger than the other 2, and gets the job done.
DS lite is more expensive with an unnecessary brighter screen and a GBA slot and runs games as well as the original does.
DSi has no GBA slot, same brightness of the screen as the DS lite was, a semi-useless SD slot, useless applications like the camera and the Mp3 player, and overall is more pricey than the others.
So honestly if you NEED a camera and mp3 player and don't play GBA games, then get the DSi.
If you want a reasonably low cost machine that has pretty much no issues whatsoever except with a dimmer screen, get the DS.
If you want a DS with a brighter screen, and slimmer build, get the DS light.