Inverters are a Tricky subject! I am an Electronic Technician, I did a bunch of experiments this winter: Hair Dryer, Microwave, TV, ect.
My conclusion is that you have Two categories of things you might want to power:
1)Low Current/Wattage: TV, Phone chargers, small Lights(ideally LED's).
2)High Current/Wattage: Hair Dryer, Microwave, ect.
...Forget about anything like Air Conditioner, heaters, stove, crock pot, ect. Unless you have 8 car batteries!
I have 2 Golf Cart batteries(225 Amp Hours) for basic needs: Lights, Pump, Fan, TV, Charging Phones, all Low Current. I run the TV off a small inverter, 300 watts, which is overkill. I might go to a 150 watt. My intent is for the Camper Batteries to last several days.
For High Current stuff, I installed a Great Big AGM battery in my truck. I plug the Camper into a 2000 watt Inverter. I use this (Sparingly) for a Hair Dryer, or Microwave. The battery is 92 Amp Hours(which is Huge!). Either appliance will run a total of 15 minutes, then the inverter shuts down. After that, I still have plenty of power to start the truck... Do NOT run your vehicle while the inverter On!!!, most alternators are around 100 Amps, A hair dryer uses 165. You will likely Melt your car's charging system.