I have been using Insignia and other Best Buy House brands in our RVs for at least ten years, all of them have been 12vdc with a wall brick to convert. They are used less than the home sets but last a lot longer than the more expensive Sony and Samsung sets we have purchased for the S&B.
You can pull your own 12vdc wires if need be but considering that a 19" set will use less than 3 amps, why not tap off a nearby 12vdc source.
When we plug in at a campground, the first few minutes the charge voltage is usually 13.5 to 14.5 volts and then the converter figures out the batteries are at full charge and drops to 12.4 or there about. I don't know about the RCA but most sets give an operating range in the products manual. Best to check there and not rely on opinion.
If I were you and there is a BB near you, I would go there and buy a 24" set for 20 or 30 bucks more if it will fit in the space you have available. Walmart has some good deals too. We did find a good deal on a 24" Insignia with the wall brick and built in DVD player for about $150 up in OR. We bought it for some friends who allow us to use their beach house almost anytime but who don't have cable and OTA on the Central Oregon Coast is virtually non-existent.