When choosing a generator, if it is to power any type of electronic device, be sure to get one with "clean" (low THD) output so that it does not fry the electronics, nor need conditioning to run them. Usually an inverter generator, becoming more common for higher output models.
As for emergency lighting and other uses, I have several LED flashlights that use 18650 Lithium batteries. Practically free to run, long runtime on one charge. I prefer flashlights that can tailstand, mine also have magnetic bases so they can be "stuck" to ferrous things like cans, porcelain sink edges, etc. for stability. Usually just bounce the light off the ceiling, can use many things as a diffuser if desired. This way, one flashlight, easy to carry in my pocket so always available when camping or in other situations, it will last a long time and there is almost always something available to diffuse the light if needed. The
Armytek Prime C2 Pro Magnet USB Warm is my favorite. Although a bit pricey, it is very rugged and has settings from "firefly" to "How the bloody heck does this small thing put out this much light?" The downside is that I have to recharge it once a year. If I ever have to grab one light for a survival kit, this is the one!
Edit to add - having a stainless or other tough metal ring bezel is crucial. I had a small Maglite LED similar in size to the one in the picture. The lights went out at work, I pulled it from my pocket, and...darkness. I was derided by my co-workers. Later, at home, I found a small dent in the front soft aluminum bezel that had allowed moisture in, killing the drive circuit. That is when I switched to Armytek, to have a flashlight I can depend on, after buying "rugged" lights that easily died from a short drop, or moisture.