This is one subject I usually stay away from and don't comment on, mainly because, no matter what, if you need to ask, you probably should stay away. No flame intended.
I live way in the hell out in the boonies and have seen tracks in my yard and glimpsed both preditors most all year round.
I'm a hunter and plinker and shoot literally 1000's of rounds a year, pistol, rifle, shotgun, air rifle, have all the major and minor calibers and all my weapons are ACCURATE, meaning if it don't shoot tiny groups it don't stay around long.
But, I DON'T ACT LIKE A PREY SPECIES, so I'm not bothered by preditors and both of these preditors usually are long gone before I ever get there. I respect both preditors fully and don't get stupid when I'm out in their "yard".
All that being said,for "personal protection" whenever I'm out working in my yard, cutting wood, hunting or just observing nature, I carry a Sig 220 .45 ACP because this one has never failed to function, a Mossberg 500 ,18.5" WITH A SKELETONISED, FOLDING STOCK (the pistol grips are total BS because you can't control or aim worth a SH**) loaded with #4 buck which is also "touched" and functions flawlessly, and another rifle or shotgun depending on the season. For the most part the "personal protection" weapons are for two legged preditors NOT the 4 legged variety. These worked for me for more years than I care to think about and I've never had to use them, but you have to understand that my mindset is self preservation!!!!
I will kill you or anyone or anything that tries to attack me!!!! But, that "thing" would have to be trying to use whatever weapon it possesses, to kill me before I would end it, and that doesn't mean a bear or cougar walking around my yard or the woods being curious or rearing up wondering what I'm up to, or some poor snake lying there trying to warm up or get breakfast.
You, also, need to get real about the "danger" out there.
Most of the stories you read about are figments of some writers fingertips on the keys or a victim of "prey activity", like running, jogging with music blasting in the ears, not looking around and mental degredation.
Again NO FLAME INTENDED, you either want to live or not. 90% of the people in the US have little or no sense of self preservation or a very media distorted sense of what is dangerous and they have been pumped full of BS by responses in forums like this one or all the other gun related sites, magazines, etc.
One story more. I have a neighbor that was scared sh**less by a cougar when he was out helping to gathering up. He rode into a thicket looking for cattle and a cougar jumped out, spooked his horse and spit him on the ground. To hear him tell it, the cougar "ATTACKED ME". The truth is more likely the cougar was in the bushes hiding and watching what was going on and he just happened to ride up on it. The rest of the crew saw what was happening and had a good laugh and watched the cat shi**ing itself as it ran as fast as it could in the opposite direction. This old boy went out and got his concealed carry permit the next week, bought himself a S&W 44 mag, 4" "CatCiller" and he is more afraid of the pistol than the cougars. You don't want to be around him when he tries to shot it because he jerks, flinches, jumps, shuts his eyes, etc. It is totally funny and just as totally frightning because he is liable to shot himself or someone else if he ever tries to jerk that cannon out of the shoulder holster he also bought and shot an imaginary "something bad this way comes". Think about it.
Buy your dream property, go live on it, enjoy it and whatever nature is available and don't pay too much attention to the scare stories everyone has, but be mindful of the possibilities.