I think the idea of a battery powered lamp is a good start.
I’m loathe to recommend anything in particular as technology is changing all the time. I’m not a great lover of rechargeables for this application as they never seem to have charge when needed.
If my power goes down I’m usually reaching straight for my old style mini maglite. The flashlight nerds really don’t like these, but they are well made, simple (no circuits or parasitic drain) light output is decent, and the “candle” feature almost unique.
I travel a lot, and can’t imagine not having one of these simple and reliable lights with me.
Second choice for me is a propane lamp. Mines a Bullfinch which is a British maker, but I’m guessing a Coleman is similar. I cook with propane and installed a spare outlet, so I can just connect up and I’m going. The light output from these is awesome and there are no issues with fumes (any more than from a gas fire).
I can connect to a portable cylinder if needed, which I always have for my blowlamp.
Next option is a “Tilley” lamp. Again, a British thing, but often misunderstood. They burn paraffin (kerosene) from a pressurised tank. The fuel is vapourised before being burnt, and they use a mantle, so the light output is much greater than a hurricane lamp.
There have been times when I‘ve needed to work in my shop without power, and these are great for that.
Final option is a traditional “hurricane” lamp. The best are the German made “Feuerhand” and I wouldn’t personally want to go cheaper. These have one advantage over the Tilley in that they have no mantle, so are theoretically more rugged, but the light output is lower, and my Dad carried a Tilley in his vehicle for decades without issues.
Finally, conventional candles or nightlights are hard to beat for simplicity. I found a cheap supply for both about 10 years back and stocked up.
Whatever you choose, have a few different options!