the big tv will run on 12 volt , the 15" only runs on AC. Is there aything to watch for when buying an inverter?
The 200 watt says non-sinusoidal and neutral floating.
non-sinusoidal means it's NOT sine wave. electronics tend to like and/or require sine wave current, so that is what you should look for in buying an inverter.
When buying a TV for 12v use, it would be best to get one that takes a 12v input directly. Otherwise your inverter changes your 12v DC into 120v AC, and then the TV changes that back to low voltage DC at some point (either internally or through a "wall-wart" type transformer), which is very inefficient use of your battery