Many vanners who have been at it very long will either build or have built a custom mount on the front of the van for their generator. Solves the storage issue as well as the theft issue.
If you have room for it inside than just go to home depot and get a cable lock to bolt it to your bumper at night. Ours runs all night, often up to 12 hours on a tank of fuel. We run a 1500 watt heater, 2 cpap machines, and our tv and game system from it. We have occasionally helped out another van or truck by latting them plug in a space heater, but it cant be over 1000 watts and we dont run the tv and games.
We also have a second, deep cycle, battery under the truck for our 1500 watt inverter. It easily runs the cpaps 8 hours when we cant run the generator, without the truck running. Of course running, it never runs out of juice!
Oh... our generator came from Northern Hydraulics. But the one from tractor supply is basicaly identical.
Hondas are great but small tank requires refilling at night and they cost 3x as much. Ours has been going strong for about 6 months now without a hitch. Just check your oil regulary and run it in level ground, point the muffler away as best you can and the noise is ok too!
Hope this helps, feel free to pm with any questions!!