you can get a UPS for your computer, to keep it running for a while. They generally have the facility to send a "safe shut down" command to the machine so it will not crash and lose or damage your work. I'd recommend a trusted local supplier with a good returns policy. For example here
In the UK it is unusual to have a power cut that lasts as long as a day, and the operators ship in engineers from all over the country, and beyond, when a major problem occurs.
For lighting, the LED camping lanterns last much longer, and/or are much brighter, than old ones with torch bulbs. They are a few pounds in Aldi or supermarts in the camping/festival season. If you have urchins who may run down the batteries, get the wind-up ones.
I would avoid candles because they start fires, especially when you might be carrying them about and have no lantern.
You also need a battery radio, and a simple corded phone. Telephone exchanges have back-up power for this very reason.
Cordless phones will not work at all, and mobile phones will probably lose signal quickly.