Depending on when you need the Nintendo and how old the child is, you might want to wait it out for the 3DS. It should be out in March and is expected to be about 250 - 300 dollars. The system is supposed to have 3d graphics without glasses.
Anyway, if you are interested, wiki has a nice comparison of the different types of DS.
http://en.wikipedia.org/wiki/Nintendo_3DS#3DS_vs_DS_Series
My guess is that it might lower the cost of the DSlite, DSi, and DSXL after Christmas. Although the price has dropped in the last couple of months on the DSi and DSlite, so Nintendo might have already factored this in.
In my opinion, for a young child, I would just get a DSi. It has the camera and image software and is not really that much smaller than the DSiXL. Both the DSi and DSiXL can access the download store as well. The DSlite is pretty nice as well for a young child. It does not have a camera and there is a slight noticeable difference in the quality of the screens between the DSi and the DSlite.
One more comment, if you already have a few gameboy advanced games, only the DSlite and Original DS will play those games. It sounds like you have younger kids, so you more than likely will not have this issue.