the above poster is absolutely correct, discharging batteries below 50% is very very bad.
my favorite batteries for feeding a large inverter and/or for engine starting are "8D" batteries. They are physically huge, cost about $150, and are used on millions of semi trucks. The batteries are built to start large diesel engines, and also run electrical loads for hours while the trucks are parked and not running. In my personal experience, i believe a single 8D to be superior to a pair of 6v golf cart batteries. An 8D weighs about 130 pounds and is about the size of 3 regular truck batteries.
400 watts is not much current draw.
I have used a modified sin wave inverter to run all kinds of stuff from rooftop a/c, microwave, freezer, electric griddle, toaster oven, lap top, tv, entertainment center, chargers, etc etc.....I've found very few things that are unhappy with modified sin wave.
Workaholic - 1400 CCA (8D-MHD)
Weight: 131.70 pounds
Length: 20.75 inches
Width: 11 inches
Height: 9.63 inches
Cranking Amps: 1750
Cold Cranking Amps: 1400
Time at 25amp draw: 8hrs