This is always an interesting question and there have been some great discussions and ideas over the years but it always boils down to the fact that there is no right or wrong answer. Why???? ... because the best answer for you will be specific to you and depend solely on your circumstances.
Having said that, there are a number of things you need to think about in coming to your decision and most of them have been touched on here and in other threads.
I'll try to remember the things that influenced me in making my decision.
1. How long do your power outages usually last? In my case it's usually hours, the longest being 2 days.
2. What do you need (want) to run and how much power does that take, including motor start-up. In my case the only thing that I desperately needed power for was 4 fridges and freezers, 2 inside and 2 outside. Some interior lighting would also be nice but not necessary. I had NG for the stovetop and water heaters. Like Bob, I also use some compact flouescent bulbs for some lighting and in my work lights so that wouln't be much of a draw on whatever generator I chose.
3. What type of fuel and how much did I usually have on hand? A typical gas generator will burn 12 to 15 gallons a day and I never have that much fresh gas in storage. I always have 30 to 50+ gallons of diesel on hand (and access to ~200 gallons at the farm) so a diesel generator made more sense. I didn't want to spend $3,000 on something for very occasional and limited use so a PTO generator was probably the better and cheaper option but if I wanted to use it away from the house I would have to load up the tractor and trailer it there. I'm getting lazy in my old age but it's still an option. A tri-fuel generator would have probably been ideal since I have NG but again I didn't want to spend that much money on something I'd use very little.
Those are just some of the things that went into my decision. Looking at your circumstances as you describe them, I'd look very seriously at a smaller tri-fuel generator. You don't want to power very much and you're going to have LPG at the house anyway so you'll have back-up fuel after the gas runs out or vice-versa. A 7.5 or 10kW generator will power the whole house (used sensibly) if that's what you need but you can get by with a lot less.
Oh!!! ... and what did I decide on?? I got a 3800 watt (5200 watt surge) gas generator and now keep 10 gallons of fresh gas in storage. It'll run all 4 fridge/freezers provided the motors don't all start at once. I don't run it continuously, I switch it on and off as needed to keep stuff frozen so my 10 gallons of gas lasts a lot longer than the outages. It's worked well for me for the past 2 years. I may change my mind and upgrade to a tri-fuel and tie it directly into the house if circumstances change but that doesn't look likely in the near future.
Lots of luck with your decision, whatever it'll be.
