So many inverter ads are so full of hyperbole it makes a person's head spin.
You need something clean so it does not disrupt the television picture, quiet so it doesn't sound like a 767 on the waiting ramp, dependable and efficient. I sure would not ignore reading customer reviews of whatever first catches your eye.
Use ridiculous overkill planning when furnishing battery power to the inverter. Meaning wire size larger than what the manufacturer suggests or supplies.
I would make sure nothing is connected to the inverter when charging the batteries.