77 watts at 12.4v is a 6.2 amp load
a 100 amp hour battery, like a group 27 or a group 31, when healthy and fully charged, can provided 5 amps for 20 hours before being completely discharged. loads over 5 amps, reduce the total amp hour capacity available of that 100Ah battery due to the peukert effect.
Lead acid batteries should not regularly be drawn well below 50% state of charge, and when they are it is very important to promptly and truly fully charge them.
the 77 watts does not include the inverter inefficiency, nor the load of the TV, and whatever else is running off the batteries at the same time.
Absorbed glass matt (AGM) are a lead acid battery, that do not require watering. Lifeline, Northstar, Odyssey are 3 top dog AGMS.
Actual gelled electrolyte batteries exist, but many people call AGM's Gel cells erronoiusly.
Actual Gel batteries can make excellent deep cycle batteries, better than wet/flooded or AGM, but they have specific limitations during charging. cross those limitations and voids form in the gel and a percentage of capacity and performance is gone forever.
Lithium batteries are becoming more affordable. I have no experience with them, so any words i type regarding them are not much more than worthless so I won't bother.
YOur power needs are not insignificant.
YOu are likely to become a battery murderer, drawing them too low, too often and not returning them to full charge anywhere near as often as they would like.
An abused Lead acid battery is like a gas tank which keeps getting smaller as it ages/ suffers abuse.
Abuse can be considered being less than truly fully charged.
a battery drained to 50%, with a high amp charging source seking voltage in the mid 14's, can relatively quickly charge a battery to 80% charged, but getting from 80% to 100% is no less than 3 hours
those 3 hours assume healthy batteries, and a charging source which can maintain 14.4ish volts for that entire time.
Idling to recharge is unwise, as the vehicles voltage regulator often decides 13.6 is fine and dandy, and a healthy group 27 will charge 3 times slower at 13.6 vs 14.7v.
If the cabling to additional depleted house batteries is fat, and the voltage regulator is seeking 14.1+ volts, the alternatort will be maxxed out for a long time, and get extremely hot.
Driving under 25mph is not much better than parked idling, in terms of hot alternator, but 65mph keeps them cool even maxxed out.
The Kill a watt meter will let you know how many KWH your devices actually consume.
1000 Watthours consumed at 12.0 vdc, is 83.3 amp hours, before the 15%+ loss from the inverter.
A group 24 battery is about 85 amp hours, and 100$
A group 24 might say deep cycle on it, but it is a marine battery.
Marine batteries are much closer in design to a starter battery, than to a true deep cycle battery.
A perfectly treated starting battery might accumulate 80 to 100 deep cylces to 50% before failure.
A perfectly treated marine battery might accumulate 300 to 350 deep cycles to 50%
A perfectly treated true deep cycle battery might accumulate 900 to 1200 deep cycles to 50% charged.
Expect real world cycles achieved to be a tiny fraction of the "lab' cycles that the manufacturer listshttps://marinehowto.com/what-is-a-deep-cycle-battery/
most internet forums have lots of extremely inaccurate information regarding the cycling of lead acid batteries.