Basically all the pokemon games have the same mechanics and flow of the game, and are the same style, unless you are going for the spinoff games which are all radically different, and IMO, not that good. If she is just starting I would recommend whatever you can get the cheapest, in case she does not like the game, this way you aren't out a whole lot of money if it doesn't work out. The GBA games can be more expensive than the DS ones depending on where you shop. You will have to trade to get all the Pokemon, so you will need 2 GBA's and a link cable, and copies of the games you need to trade from. You can't trade from GBA to DS, but you can transfer from your GBA games to your DS games if you have a DS Lite or DS Phat. But you can't do that with a DSi or 3DS since the systems don't have a GBA slot. A lot of kids have a love hate relationship with Pokemon, so I would just start with one and see where that goes.
Overall I think I would skip Diamond and Pearl, although they are very good, but Platinum is the 3rd version of Diamond and Pearl, so I would just get that one and skip out on the previous 2. Keep in mind that everyone on the GTS aka wifi trading only wants ridiculous trades, so if you need a pokemon the best way is to just put up a pokemon of your own and wait until it gets traded for whatever you want. The ridiculous trades will lead to disappointment for a child who just wants to trade regular pokemon online.