Jeagle88, PistonCupChampion put you in the right direction on the camera choice. The batteries are just rechargeable AAs. You can pick them up at most supermarkets/drug stores as well as Best Buy and Radio Shack. The SX130 will eat through regular alkaline AAs, but the rechargeables will more than double your shot count. A 4GB or 8GB SDHC card should be plenty of storage. You'll want one rated Class 4 or higher for recording HD video.
The camera is bulky, though, so you might want to make sure she doesn't want a tiny camera for her purse.