Generators are something that I have a little experience of, sadly. I would say avoid the inverter ones unless you have to have something small and quiet; they are expensive to buy, prohibitively expensive to repair and are much more likely to breakdown when you need them than an old-style genset.
I wouldn't go for gas (LPG). They might be economical to run compared to petrol, slightly more expensive than diesel gennies; but they are very hard to get repaired/serviced because most engineers won't touch them unless they happen to be specialist gas engineers (I couldn't find anybody near me that would even look at mine until I removed the LPG conversion and didn't mention that I had ever had it there!). The way the conversions work usually means that even if the LPG doesn't work, you can normally still run petrol in them; assuming it's not a stand along LPG fuelled machine
If you are likely to be running it for many hours and frequently, then diesel gennies are great. They are bomb proof and easy to fix yourself (relatively), as well as cheap to run. Old lister generators are excellent standby power units and really cheap, but you need space to put one. If you have heating oil or a diesel vehicle, then fuel is not so bad and stores for a year or so without problem
Petrol gennies are cheap to buy and for occasional use probably the most sensible choice. I would suggest using an alkylate fuel (Aspen is what I use i all of my petrol engines including a couple of generators) as it stores for years in the bottle (I'm currently working through a bottle I bought about 6 years ago and it's fine) and doesn't mind sitting in the machine's fuel tank. I've started petrol engines after 3 years without draining or changing the fuel and had no issues.