To properly run the microwave you are looking at 1800+ watts of sine wave power and four batteries connected with large wire as it will draw 160+ amps. I recommend GoPower brand inverter but Xantrex and others are fine. Stick with sine wave only.
You have 12v supply so you need 12v inverter.
If you can make coffee and popcorn on the stove.... installing a 150w/300w inverter to run small stuff would be a lot easier. Use the generator for the big stuff.
I actually have a Xantrex Prosine 1800 to power the MW and one added outlet in the kitchen. I also have a GoPower 300w sine wave inverter wired to the existing outlets to run the tv, dvd, laptop, cell phones, games etc.
