I have a .22 revolver we like to plink with.
I carry a G26 or something along those lines on me, depending on how "woodsy" the place is that me and my sons are camping in. Meaning, if it's a popular kind of camping place with lots of people the G26 is fine because all normal CCW concerns apply. If we are "out there" somewhere I might carry something bigger.
I always bring a Mossberg 590A1 with Brenneke Black Magic slugs as the first four shots with 00 Buck for followup. Would work on just about anything with any number of legs I would ever encounter in the lower 48.
That stays in the tent with me at night.
(Exceptions Bigfoot, Swamp Apes and the Cupacabra of course. I would need a 10mm for that but I am afraid of getting sued for destroying 20 square acres if I should have to use it.)
I don't know if there is a best all purpose camp gun since like any type of gun it's hard to say there is a best all purpose anything. They seem to all fill roles. I guess a shotgun is one of the more flexible things.
I would like to have a GP100. That would be fun and useful.