1. Forget 12v TV's. Way too expensive and poor quality.
2. Sounds like you won't be plugged in to electric, so definitely consider an inverter and ample battery capacity.
3. Does your rig not have a genset either? Another consideration, but now your costs are starting to really add up!
4. Running on battery, the TV's power consumption should be a top selection criteria. Other than that, buy cheap! At less than 42", HD picture quality is nearly indistinguishable from one TV to another. 720p vs 1080 makes no difference on smaller screens either and 720 TV's are always much cheaper.