you may want to sell that 13" TV and get a LCD monitor... unless you want that huge TV velcro'd to the dash.

I'd say to get something a little more suited to the car to start with.

A power inverter is the way to power them... theres no other way really to get 120 volts in the car. You dont need anything huge... If you really plan on keeping the TV, go with something relatively large though, like a 200 watt inverter, TV's use a lot of juice on start up, and you dont want to overload it. Something with that power should have 2 outlets on it too.