I'll add that on our little camper boat, I run the small fridge on an inverter. It is a 3.7 cuft haier. It pulls 5-7 amps on start (about 1 second), but only 1.1 running. With only two adults, it is not opened and closed constantly, and may go for hours without cycling. A little honda EU1000i runs the whole show, runs the 5000 btu AC, and a little portable electric 1000 watt heater when needed. Sometimes we go for days without cranking the little generator. The large marine battery does a good job.
I use a Black and Decker 750 watt inverter. It is the first one that I found that the cooling fans do not run except when the inverter has a large load. I'm on my second one, the first started making fan noise, so I replaced it. They don't make this exact model anymore, but I found a new one on ebay and carry it as a spare. Plus, if it comes to it, I can try to replace the fans in the first one.
This is over 12 years. Anytime the generator or the outboard motor is running, the battery is being charged. The inverter sounds an alarm just below 12v. It has worked out great for us. I have 2400+ hours on the generator, only oil changes every 100 hours, nothing else. Only 1160 hours on the outboard, so there is more "sitting" than "traveling"....
This little generator weighs 29 lbs. The next one up, the EU2000i weighs 50. When and if I have to replace it, I will go to the larger just so it will run the microwave on high power... Popcorn and such...
I also have the TV and antenna powered from same inverter, sometimes we watch TV waiting for the real STARS and moon to come out...

Mainly, try not to open and close the fridge more than necessary. Either put cold stuff in to start with, or have a long run before you cut power. We freeze water bottles and fill as much as possible with them, leaving room for beer of course... and food...
I do wish I could find a newer super efficient inverter, one that uses about nothing until it gets a load.
Good luck! Woody