After someone linked on here a while back I bought a 19" kogan LED television at the beginning of the year and have been very pleased. Real world measurements are around 1.9A and 200mA standby (unusual to go so low on standby, my older 11" TV stayed around 2A on standby as well as turned on!). I plug the Kogan straight into the boat's supply, no messing with inverters, they are not necessary for this set.
I have the TV and boats radio attached to a Triax UFO aerial up the mast, I get a stunning picture most of the time, but can lose the odd channel at low water on a miserable day.
If 19" is too large, my 11" TV came from maplin, really handy size to stow. That's not mine, but I might consider selling it at a similar price, though it is handy in my study for watching Question Time on Thursdays, so I might be loathed to part with it