I don't imagine this will help you pick an inverter, 97grandby, but I'm responding to the more general thread title....
In our old van camper I just take along a 150-watt West Marine inverter to plug into the cigarette-lighter socket. I mostly use it to charge up our two laptops (I had tried an aftermarket 12-volt charger but it was much slower). We don't have a furnace, fridge, or water pump so don't even have a house battery in that camper. We just run off the vehicle battery and depend on the alternator to charge it. (And of course can't have a microwave, toaster, etc). We also charge the camera, Inreach, GPS, two dumbphones, a micro-starter battery, and run an over-counter fluorescent light, Fan-Tastic fan, and Smittybilt air compressor off the vehicle battery (and alternator). But we don't do it all at once!
I bought the used Hawk shell and F150 as a package. The rig came with a Xantrex Pro-Sine 600 in the truck's cab and it was used to charge the camper's battery with a very high quality marine charger the previous owner had for his boat. The charger wasn't part of the deal so I bought a Xantrex one and use the inverter and charger to charge the (single) house battery. I don't have a fridge, don't use the furnace much, minimize use of the battery and move every day, so it works for me but I don't know that I'd recommend this setup to others.
I don't like the fan noise of the ProSine in my cab in warmer weather. The fan comes on whether I have anything plugged into it or not (when powered on). I also have to be careful to not leave it powered on when the truck is parked for more than a day or so as it will drain down the vehicle battery just being powered up (without the charging load).
I also didn't have a great experience in trying to get tech support from Xantrex. (If others have had a different experience, please chime in--- I'd love to hear I just had some bad luck.)