That shield, an uno and a wifi shield would be the obvious starting point. Check though that the shields don't have any conflict in the pins they use, If they do, it's probably not a show stopper, but you will have to wire them up manually, rather than just plugging them together. In this scenario you may need to tweak any libraries that those shields use too.
For power you can either regulate the supply from your batteries to 5V and provide it on Vin or you can provide it via the barrel connector. In the latter case, you'll need a minimum of 7V.