storing a car for 6 months

should I add a fuel stabilizer to the gas?

Yes, unless you want to run the tank almost dry and fill with non-ethanol fuel. If not, use a stabilizer, per the recommended allotment and FILL THE TANK. Less air means less water condensing on the inside of the tank and causing rust.

BTW, ethanol fuel (what you run, normally, in your car) has a shelf life of 3-4 months, non-ethanol is a year. Ethanol will separate… water towards the bottom, dinosaur on top.

You may also want to do an oil change and drive it for a week before parking. Good to get fresh thruout…