Small Generator choice for 5W

Any generator that has a 2 cycle engine is likely very small, cheaply made, and noisy. There are a bunch of them around from Harbor Freight and other such places. I would avoid them. Yamaha and Honda both make excellent small generators that are quiet, fuel efficient, and will last many years with proper care.
I wouldn't try to use propane for the generator normally. You can get kits to convert most any gasoline generator to use propane so you could do that in a pinch. But, for most use I think gasoline will be easier to obtain and handle.