the OP did not mention 'inverter'
although he did mention TV
my suggestion is to make a list of power requirements
how many hours of TV
how many hours of lights, how many lights
Furnace ? blowers are a big power user
water pump, is minimal except for showers
even ten minutes with a 6amp pump is not going to break the 'battery bank'
even with say a family of FOUR
for many including my self, solar is a help, but not a cure all
a 'perfect' system would put BACK everything you used between sunset and sun rise,
while also supplying all the power used during the day
there are very few 'perfect' systems, mine is not perfect
do the power audit, and we help you figure out, what can help you limit your generator run time
example 23" TV 40 watts per hour 3 hrs, thats 120 watt hours or approx 10ampHrs from your battery bank
typical 11w light bulb 0.9amps
(2) bulbs 4 hrs 88watt hrs approx 8 amphrs
water pump ?
fridge controls ?
etc..
typical TT parasitic use 35 ampHr per day
in todays always connected world
cell phones, tablets , laptops etc.. for a family total more power use than the avg RV uses