I did a lot of reading about this when I bought a generator for home backup, and I wanted to keep a 3-day supply of gasoline (out in the shed, not the house!). For storage of more than 30 days, all of the small-engine manufacturers recommend either using a fuel stabilizer with a full tank of fuel or draining the fuel system completely.
The gasoline sold now is not the same stuff as 20 or even 10 years ago. It has more volatiles in it that evaporate and change the characteristics of the fuel, and a fuel stabilizer slows, but does not stop, the evaporation. The maximum time you can keep the fuel is two years with a double dose of the stabilizer. Without stabilizer, all the gasoline companies say use it within 30 days.
Depending on the car you may be heading for problems by not driving the car much, but that is better than not driving it at all. Try to keep the fuel tank full to reduce water condensing inside the tank. I learned about this when I owned an airplane that I flew about once a week, and was told to always fill the tanks when putting the airplane away. What happens is that cooler temperatures overnight cause high-humidity air to be drawn into the empty volume of the tanks, and the moisture in the air will then condense inside the tank.
If the tank is kept full, there is less empty volume for air to move in and out of. Since I gather you just drive your car short distances a few times a week, I'd say keep the tank above 3/4 capacity and you should be all right. I gather you use perhaps a tank of gas a month. If that's the case fill it up once a week or at least once every other week. What you want to avoid is having a near-empty tank for long periods of time.
I once had a pickup truck that had two tanks, I didn't use it much for long periods, and one tank rusted through from the inside from water accumulation due to condensation. It was about a $300 replacement ten years ago.
If your lawn mower, tractor, etc. is stored with a full tank you might get away with not using a fuel stabilizer or draining it, (including the carburetor) but I've always drained mine.
If you're going to store it, the owner's manual for your car should have a section on long-term (more than 30 days) storage. If it was me, I'd use a fuel stabilizer and make a point to drive it at least every other week. Don't just let it idle in the driveway for ten minutes, that's worse than not running it at all. The engine and drive system need to get up to full operating temperature for a while to evaporate the water that condenses in the engine and transmission. This means drive it for 20-30 miles at highway speed if possible.