Refrigerators use compressors which often require 5x or greater power to start. You will need to check your generator's peak output to confirm that it can start the refrigerator's compressor. In my experience only relatively small refrigerators can be powered from 1.5kW / 2kW units.
Depends on your power needs and how often you plan on running it. Gasoline fuel doesn’t last as long as propane, but makes more power (you’ll often see different wattage for each in a dual-fuel setting).
If the generator is mostly going to be sitting around with infrequent usage, either go propane or research gas fuel stability and storage treatments.
Maintenance will depend on the model, but it’s going to need spark plugs and oil changes at a minimum.
Do you have any size or transportation constraints?
Gasoline degrades more quickly than propane.
When I looked at options for keeping a couple days worth of fuel around (with no gas-powered yard tools to necessitate fuel turnover), propane seemed like the more attractive option.
I was also storing said fuel in an outbuilding with venting and pretty far back on my property.
If you're regularly buying and storing gas, your math might math differently.