I install solar, battery, and generator systems for a living. "Solar Generators" are kind of a gimmick. They do technically generate some power and can be used for running a refrigerator or some lights but they are not even in the same league as a gasoline, propane, natural gas, or diesel generator.
A home solar system with battery back-up can be made as large as necessary and can run everything you mentioned but it's going to cost you around $20,000 at a bare minimum, likely twice that. The good news is that it qualifies for a 26% federal income tax credit and it can reduce or eliminate your electric bill if sized right.
For your use I would go with natural gas if you have it and propane if you don't. The typical home-sized propane generator requires a minimum 500 gallon propane tank. This is larger than what can be mounted up against the house per fire codes so it must be either buried or sit out in the yard.
Diesel is great but much more expensive and unnecessary for most residential use. I personally have a 20 kW Kohler with a John Deere diesel engine. I got it on Ebay for $3,400. If you don't mind used their are always older commercial generators for sale on ebay and craigslist. They are often in service at a commercial facility for 20 years or so with very little run time and rigorous maintenance. After so many years they are simply replaced with a newer one to maintain reliability for the facility.
I highly recommend Kohler generators. I have heard too many horror stories about Generac to count.