No idea what contract or phone (phone is personal preference in many ways since they'll all do what you want, though you're clearly going to want one with a good camera) - I'd think your best bet would be to buy the phone outright and then get a PAYG SIM card in the US to keep costs down. If you're going to be storing photos and videos on the phone, clearly it's going to need a decent amount of storage - it might be best to look for one which you can plug an SD card into - a few of these will let you carry loads of storage around with you (32 GB SD cards are pretty cheap these days) in a small package. This of course rules out an iPhone. Multiple SD cards also minimise your losses if the phone were to get lost or stolen - it hopefully won't happen but a friend of mine was gutted when the laptop she was storing all her photos from a year of travelling on got stolen in Thailand.
For battery life, I'd think you're going to need something like
this to allow you to keep the battery topped up when you're away from the a power source - this is just an example, I'm not recommending that model from personal experience but it does seem to have some good reviews on Amazon. (though obviously make sure whichever one you get supports whichever phone you choose!).
This article might be useful - it's based around the iPhone 5, but actually has some quite detailed info on the various networks in the US, especially this note on the second page:
Rural KY/VA/WV/TN:[/b] Appalachian Wireless runs a relatively slow 3G network in some very rural areas on the border between these states, and its plans only make sense if you don't travel much. Choose it if it's the only good coverage in your holler.
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