If it were me I would just keep a close watch on the battery DC VOLTAGE when running things off of it using a real DC MULTIMETER . When it drops down to 12.0VDC then you should stop using the battery...
This will tell you when you are getting close to draining the battery below 50% charge state. Then try to bring the battery back up to at least 90% charge state during the daytime hours when the sun is high. You want to get the battery back up to the 12.5-6VDC level after it settles for ten minutes or so.
Your LED lights will not be a problem for battery drain but the the 35WATT LCD TV will draw around 3 AMPS or so... keep in mind you have to put back into the battery what you have taken out. The solar panel will only produce around 6 AMPS of usable charge power so keeping it re-charging your battery all afternoon whenthe sun is high should re-coup what you have taken out of it hopefully...
This is handy charge showing what the battery DC VOLTAGE reading is verses what the charge state is. This is not exact but will give you a good idea what is happening as it occurs.
Most folks would not dream of camping off the power grid with just one battery. The best setup for lots of battery power for the bucks spent would be two each 6VDC Golf Cart GC2 batteries. They cost around $70-$90 each and are available from SAMS/COSTCO here in the states. Two of these together connected in series will give you around 220AHs @ 12VDC.
We camp alot here off the power grid and do alot of things out in the country side and mountain trails etc. When we get back to settle in for the night the HDTV and checking in with family and paying bills etc comes in handy... I am also a Ham radio radio which will consume alot of power if I get into it pretty heavy.
It is hard to think you will only live off of what comes from the solar panels. This is only there when the sun is out. The idea should be to run everything from batteries and use the solar power to just charge your batteries back... To get 20AMPS of solar power will require at least four 100WATT panels if you want to re-charge your batteries in a quick three hour time frame using smart mode charging techniques.. To charge my three deep cycle batteries in a three hour generator run time I have to use my PD9260C 60AMP OUTPUT Converter/charger being run by my 2KW Honda generator. If I only had the one 80WATT Solar panel the 6AMPS usable DC current coming from it from noon to lets say 4-5PM would not get the job done in two or three days time...
Just more things to think about...
I always try all of these things out in my back yard before I commit to being stranded in the back trails somewhere hehe...
It does take some planning for what you want to do - you just can't run for the off trail places and expect to survive the night with battery power left. It will get dark on you around 10PM at night is what always happened to me... Then I have to deal with momabear haha...
Momabear is from Texas - they always shoot first and then ask questions...
Roy Ken