The difference between a DS and a DS Lite is at least size. A regular DS is getting pretty old. People that have a Lite may just call it a DS though. The difference between a DS Lite and a DSi is the camera, among other things. The DSi is the latest and greatest. We just have the DS Lite.
You will need to buy games. I think it was DD8's 6th birthday or near it when she got one. It was a good purchase. It keeps them busy in the car. We have three and play together.
The DS will come with a charger and an extra stylus. I highly recommend getting screen protectors- you can buy them for iPhone or whatever, they don't have to be specifically DS protectors. We got a car charger because so many times they are going dead on the road. We also bought a bunch of extra styluses on eBay. Some of our original ones were getting loose and not staying in the holder. They were cheap, came from China or Hong Kong but I took a chance and they work great. They fit snug like they should. So now we have like 40 or 50 extras in a rainbow of colors! You won't need to worry about that for a while though...
As for games, she liked the Disney Princess Magical Jewels, Build-A-Bear, Disney Bolt, the Petz games, Mario Kart, Tinker Bell.