I'd pass on the mare's leg, and stick with a 12 ga. The .357 represents a minimum threshold if you are carrying a handgun, but there is no need to limit yourself to that extent when carrying a long gun. Pump shotguns tend to be less expensive than rifles that are suitable for self defense. A 12 ga provides the added versatility of firing less lethal ammunition such as cracker-shells and rubber bullets, although combining less lethal and lethal ammunition in the same gun is a practice I disapprove of for a bunch of reasons. Given the current fire situation in BC, it behooves anyone using cracker-shells or any other pyrotechnic to use extreme caution. If you fire the cracker-shell straight up, it reduces the chance of fire, and eliminates the problem of the cracker exploding behind the bear.
For a new out of the box, reliable, low cost gun, consider a Mossberg Maverick 88. At one time I had a low opinion of this gun, but the recent ones I've handled and fired leave nothing to be desired. The actions cycle smoothly and the triggers break cleanly. If you're willing to spend a bit more, look for a new or used Mossberg 500 or better yet a 590. I carry a 590 with a Magpul SGA buttstock, which uses spacers for adjusting the length of pull. Avoid guns with very short barrels, where you hand could inadvertently slide forward off the forend and in front of the muzzle as you fire. The damage would be life changing, and if in a remote area, might not be survivable.
Sights on shotguns are a bit of a problem. Low cost guns frequently have bead front sight mounted directly on the barrel. This puts the bead lower than the height of the receiver, and will cause you to shoot high, if you put the bead in the center of the target. Consider putting rifle sight s on your gun if it doesn't come with them, or a pedestal under the bead to raise it above the height of the receiver. A technique that can be used is that once you have your sight picture, depress the muzzle until the bead disappears from your line of sight, and the moment that happens, press the trigger. While its not intuitive, it works after a fashion if you practice. Some folks claim they just need to hide half of the bead, so they don't entirely lose their aiming point.
So I'm a little concerned with your desire for a "beater gun". In my experience, which is considerable, too often folks buy cheap guns, then neglect and abuse them, because they're cheap beaters, to the point that they won't function when they need to. In that condition the gun cannot save you. What is your life worth? Buy a good reliable gun. Don't worry about using it in the rain, it will tolerate that provided its wiped dry and oiled at the end of the day. Be aware that in wet environments shotgun shells tarnish quickly when exposed to the elements, and become difficult to cycle. So on extended trips, ensure the gun is unloaded at least daily and the shells from both the magazine and side saddle are wiped dry before being reloaded. Both the bore and the magazine should be patched out if they get wet. If you are operating in steep, slippery, rocky, country, a heat shield will help protect the thin barrel from being dented in the case of a fall.
The correct ammunition for bear defense is slugs, buckshot has no advantage except in circumstances where over-penetration might endanger others; I'm thinking here of towns and crowded camp grounds. At the range at which you will shoot a bear, the pattern of the buckshot will still be very tight, and the gun must be aimed with the same precision as a rifle. Consider that as a rule of thumb, shot patterns open up at a rate of about an inch per yard. A bear can't hurt you if it can't touch you, so the purpose of shooting is to prevent the bear from touching you. That suggests a range of say 3-5 yards, and at 5 yards the pattern is unlikely to be larger than 5". Don't shoot center of mass, shoot for the spine or the brain. If the bear is broadside shoot for the point of the shoulder or the hip. Once he's immobilized, he can be killed with a head shot. I like Rottweil Brenneke slugs, and Challengers are my second choice. In buckshot, the stuff that provides the densest patterns in my gun are 3" Federal Premium 00 Buck. I keep the magazine filled with slugs, and have 6 buckshot loads in the sidesaddle since this is the gun I use close to, and around town.
If you intend to shoot less lethal rounds, fire them singly, loaded through the ejection port. If you buy a gun like a Winchester Defender, the elevator might have lips that make it easier to load from the magazine, if so carry the gun with 1 round short of having the magazine fully loaded, then single load the less lethal round into the magazine and cycle the action to chamber it. An extended magazine offers little advantage in the bear defense role, and when fully loaded adds weight to the gun, making it more fatiguing to carry for long hours, and increases the chances of it being left behind when bear sign is not evident. The gun should have a sling, a simple nylon carry strap works fine, I prefer 1.25" slings to the 1" models. The important thing is to practice loading and unloading the gun. Once you get it, do it in the dark, do it upside down. Work out a reliable system for selecting a shell that is different in type than what you have in the magazine, and get it in the chamber. This might be through the ejection port or fed from the magazine. If you need another one, you have to cycle the action only part way so the fired round is ejected, but the subsequent round in the magazine isn't released. If it is, roll the gun on its side to drop the the round from the magazine out of the ejection port.
Hope this helps.