Bah, just walk around with candles.
Our first priority is the fridge/freezers. We have wood heat. So we are warm, cold beer, and a BBQ (with sideburner) for cooking. No need for A/C in my climate.
If it get's really long or we run low on genny fuel then we fire up the RV. In the RV we have hot water, showers, fridge, freezer, furnace, all on propane for days until I need to charge up the 12 volt battery which can be done with the automobiles.
Sounds like me.
I've got a little 2000 watt Yamaha inverter generator. I don't actually need the thing, but I thought I might use it to power my main PC or most of the AV system to watch movies or play video games if utilities are cut off for a long period of time.
I can't really think of a reason to worry about heating or air conditioning. It would take one hell of a generator to run the units handling this building.
As for refrigeration, I don't really need it, but it's not a problem. My Engel 45 will keep things as cold as I want for as long as I want with very little power use.
Water? If the Tar River runs dry, I've got other problems to worry about.
I can heat water, but it's super-complicated. You've got to use this strange "fire" stuff. Terribly difficult. Of course, I can just use my ceramic filter if I'm feeling lazy.
Beyond sanitation, I can't really think of a reason to worry about hot water. Waste of fuel, if you ask me. You could be playing video games.
As for cooking, I use a fire pit on occasion. It's fun, and the food tastes wonderful. Of course, again, if I'm feeling lazy, I've got a Weber Genesis and three tanks of propane, as well as a MSR Pocket Rocket and tons of fuel.
I never really thought much about lights. I have a "Candle Lantern" and a bunch of spare candles. If you don't own one, you should. They are outstanding.
I suppose it would be cool to flip a switch and power the whole building, but I'd rather keep any fuel I've got for mobilization. All my tanks are always full, and the jerry cans are rotated regularly.
So, I suppose my answer to the original question would be a couple of outlets to run entertainment electronics.
That's the way I look at things.
That said, if you are deciding what to power during an emergency, focus on getting one specific area fully operational.
Abandon the rest of the house, and keep that room at operating temperature, with all your conveniences functional. If you want to use central climate control, you'll need a thermostat or temperature probe in the room. Pick a room that's more than one wall away from outside air at all sides, add extra insulation, and be sure you've got water access.
Having a big generator is pointless if you run out of fuel trying to keep an entire house comfortable and a bunch of **** you don't actually need running.
You need this stuff planned and set up in advance if it's to be worth a damn when you need it.