Good thread.
Much has already been discussed and thought out.
Where you live and your power consumption will probably determine both the size and fuel that you choose.
Living in rural Vermont, natural gas is not an option, and propane, while available, is not something that I could bury at my location to prevent cold Vermont winter issues.
In the past week or so, we have had two power issues. The first was the result of a very heavy, wet snow storm, which caused outages due to branches/limbs/trees succumbing to the heavy weight. Our outage was very small and short lived, and I used my 2KW inverter generator to provide some lights for just over 4 hours in the evening. However, 3 days later, we went from 42F down to 8F in just over 12 hours, creating strong, gale force winds, 50-60MPH locally, which pummeled the area, again taking branches/limbs/trees down. My power went out at 3:42AM and I reported the outage. Luckily for the power company, there were already out of state crews here from the previous storm. It was nearly 2 hours later before the power company reported that it would be 12-24 hours before power might be restored. Due to the continued high winds and low temperatures, I elected to hook up my PTO generator, via double throw switch, to my home. That way I would have power for the furnace and fridge, and whatever lights that I chose. During outages, I elect not to use high draw appliances like dryer or electric range. I have a removeable portable 2 burner stove from my camper that I can run off propane for stove top cooking. As the day wore on, the power company reported over 58,000 homes without power. Huge trees all over the county were either snapped or uprooted. Radio and TV tried to keep everyone informed. We were constantly calling and checking on neighbors and the elderly in our area, giving them the option of using our house as refuge. Originally we were finally given an estimate of 6:45PM for power restoration to our area, but due to continued high winds and temps dropping below 0F, the power company sent most crews home and extended our restore time to 6:30PM the following day. Needless to say, I continued to run the generator. I keep my home thermostat at 68F, which normally is comfortable, but with the winds howling, the furnace was cycling on and off. Running the generator on an 'as needed' basis would have been insane. Each and every winter, in the event of a power outage, I fill all my available 'diesel' cans with winter grade fuel. I have about 35 gallons of storage. My power was restored at 5:45PM Christmas Eve. I burned approximately 15 gallons of off road diesel over the course of 38 hours. I was much more lucky than many. There were still over 1200 homes without power on Monday morning. I had even loaned out my 2KW inverter generator and two extension cords to an elderly neighbor who had no power, but luckily had a wood stove. During this outage, my tractor finally broke the 1000 hour mark. While some on this forum might question the sanity of running a generator 24/7, living through a storm like this one might convince you.