In our open living and dining area, we use 2-3 large Siege lanterns. In bedrooms we just use one. I have a small Siege, because it's cool, and has a magnetic base. It's OK in a bathroom but not that great in large rooms. My wife bought a 3 pack of Black Diamond Remoji lanterns, and while not incredibly bright, they're easy to hand up in smaller areas.
If power outages last more than a few hours, it's a good idea to have lanterns in every room so you aren't carrying it around of leaving someone else in the dark.
ETA: handhelds are good to carry with you during an outage, but suck for most life tasks.
I've got a Black Diamond headlamp and I like the brightness/throw for night hikes, but it's more complicated than it needs to be. We've also got $10-20 headlamps from Target that work as well for most things.