There are 5:
DS Original - chunky, looks slightly dated compared to others. Can't buy new any more I don't think but will be the cheapest second hand if you can find one. All of the DSes can go online but this is the only one without a web browser, you can only use it to play the games online. Hardly any choice of colours.
DS Lite - smaller, intended for younger children mainly. A basic version of the more updated ones. Probably the most popular in our shop. There are a few different colours, the pink and blue are washed out looking IMO. Backwards compatible with Game Boy Advance games, so you might be able to pick these up cheaply at car boots/in charity shops etc although they won't be able to use the stylus with them, just the buttons.
DSi - Same size as the original one. Has a camera. The current "standard" model. Lots of bright nice colours. Not compatible with the older GBA games.
DSi XL - Really nice big screen on this one. Also has a camera. Aimed more at adults or older children. Other than the large screen/size, it has no extra features to the DSi. It has more understated/"adult" colours like brown, wine red etc alongside the usual pink, green, blue. It's also not compatible with the older games.
3DS - obviously the big selling point is the 3D. You can turn the 3D off so if you were wanting to share it with him or didn't want to shell out twice for an upgrade later it might be worth getting one now. You can play all of the normal DS games on this as well as the new 3D games. None of the others can play the 3D games. Again, this one doesn't play Game boy advance games. Camera can take 3D photo/video, which is quite cool.