I have this setup for my "entertainment" system. A few questions to ask is how many watts the TV will need to run and what else you will run with it.
For example: we chose a 24" led TV over a 32" because the 24 used approx 30 watts and the 32 used more like 80. Actually the 24 was cheap as hell on Black Friday and I am "roughing it" after all! Also the blue ray player uses 5 watts. So plug it all in to a 400 watt inverter that I already had and even if I'm using 100 watts with inefficentcy it only comes out to about 8amp/hrs.
Most group 24 batteries are 84amp/hrs so it's not a huge drain when boondocking. Need to remember to turn off inverter when not in use. Wired it all to provide power to TV all the time and when plugged into shore power, trailer charger will keep up nicely.
2014 Stealth Evo 2850- "Woodstock"
2011 Toyota Tundra Rock Crawler TRD 5.7- "Clifford"
2013 Honda Accord Coupe V6 w/Track Pack- "Julia"
Just glad to get away