I'd carry a small shotgun or large revolver (loaded with shot in at least three chambers). When we lived in the boonies out here, we didn't go far on the property without a rifle. Coyotes, bobcats, the occasional cougar, and large, aggressive dogs[1] were always possibilities, never mind poisonous snakes, rabid smaller animals, etc. Never had to shoot anything, but neighbors occasionally had to. I did have to scare a vicious dog off once by shooting at the ground near it. It had attacked our daughter and the neighbors were sloppy about chaining him up. They thought I was shooting *at* the dog (it was tempting, but that particular day he was just trespassing), and kept him on their property after that.
[1] A neighbor (sheriff's deputy) caught those dogs rampaging through his herd of goats. After he shot them (the dogs), he took photographs of everything, then hauled the dogs in his pickup to their owners' house, put them on the porch, and rang their doorbell. (They had been warned, as the dogs had gotten out and attacked people, pets, and livestock before.) He made it clear that they had (some number of) days to pay damages or he'd have them arrested and sue them to boot. They paid up and upped their fence game before getting more dogs. Sad.