I can't believe almost 40 posts of no relevance to the OP's question, at least there were a couple... his budget was about $500! Why are you posting links and info for $8-10,000 units? Not at all helpful!
I don't care if you can run your shops, 4 welders, and two freaking homes with your generator! The OP is looking to run essential items when the power goes out, and use it up at their cabin.... which means PORTABLE!
Here is a great AFFORDABLE unit that will meet your needs.
Firman H?7552 75??W/94??W Dual Fuel Electric Start 5?A Generator Manuf FactoryPure
Here is another, right in your price budget:
Pulsar 65 Peak/55 Rated Watts Gas/LPG Dual Fuel Portable Generator RV Ready | eBay
I have run this unit for my 3600 sf house, running a 27cf refrigerator, 21cf freezer, minimal lighting, and the propane fired forced air furnace. The refer and freezer were only intermittent... they don't run continually. Same with the furnace....
The shortest run time I got on a 40lb tank was 20 hours. The second tank, I got 26 hours.... running the previous equipment.
I will NOT run any gas through the generator unless absolutely necessary. It starts on propane within about 2seconds of pushing the start button. I have now wired in a manual transfer switch to the house panel so I can be very selective with what I turn on.
I purchased mine for $699 at Costco on sale. You can find some smaller ones (wattage) for a little less. LOOK AT THEIR WARRANTY! Best in the business for portable generators.
Good luck, I hope you find something suitable.