I have an awesome 100W folding solar panel that I bought for $200 that has the charge controller built in. The furnace uses around 100W by itself, so I figure that as long as I can get as much sun time during the day as I do furnace time at night, we'll be fine. We've never had an issue, even with a single battery, but we also have a generator. $1000 for a solar setup is a tad steep, unless it's 1000W and has the charge controller built into the trailer.
As for TV, if it's an LED TV, it will use a small amount of power. A non-LED LCD TV will use 2-3 times as much as an LED TV. In my case, my 32" LED LCD TV uses right under 30W.
TV: 2013 Ram 2500 4x4 mega cab w/6.7l Cummins
Trailer: 2013 Palomino Puma 27SBU