The biggest load I was able to run off of an inverter is the fridge.
After repeated failures, I replaced the "modified sine wave", with a 1.5KW pure Sine wave inverter.
No problems since, but I also installed 4 LARGE deep cycle batteries to power it.
Take the amp hours of a battery, divide in 2, then divide by 10, THEN divide by the total load, (current of EACH device plugged into it). That's how many hours of run time you have.
Small TV's, and laptops, and other small devices that are powered by "wall warts", often are actually powered by 12VDC. look at the fine print on the wall wart.
You can usually buy an adaptor that has a cigarette style plug, and power them directly.
I would save the inverter for a specific appliance that just doesn't come in a 12v version, and doesn't take too much power.
Our current technology just doesn't have the power storage to replace a generator with an inverter, it takes too many batteries.