I personally find about 200-400 lumens works well for me during general, sustained tasks.
But it really isn’t as simple as lumens… and for camping, a level of redundancy is important for safety, especially in bear or cat country.
I’d really recommend a floody, efficient headlamp (w/ a low moonlight!) + spare cells a throwy pocket/holster light a low lumen red/amber light as minimum gear.
The thrower, as others have mentioned, should be capable of an ANSI throw rating of at least twice the range you want to see. I recommend a simple C8 to a lot of people, but a simple UI, dare I say tactical, is best here. Single mode if need be. Dual switch might be best (forward click tail with side mode changing) and ideally 120kcd or more. A C8 with an XHP35 HI yields a broad, bright spot around this number. Think of it as your ‘oh sh’ light.
Carry spare cells in a proper case, never loose.
If you can swing it, a multi cell light with a good diffuser (aka lantern style) is a good idea.
P60s are great for camping IMO when you want specialty light sources that’ll rarely be used (ie red/green/etc) and you want to pack lightly.
Something like a C01R is a perfect camping/hiking companion imo.
AAA/AA back up lights should match or exceed the number of people in your group.