Firearms are tools and different situations call for different tools. Its not easy finding something that can do everything great. From what you are looking for I think a 12GA pump action shotgun would fill your needs best. Regardless of what you end up getting your going to need to put in some training time to learn how to run whatever system you go with. Down in Texas I can pick up 100 rounds of Lowbrass 12GA for around 20 bucks. If bears are a serious concern 12 GA slugs are goin to be what you want to load it with so I would recomend you get something with some kind of sighting system like ghost rings or rifled sights. I wouldnt recomend a rifled barrel though as I know i would like to be able to still shoot buckshot through the gun for home defense or if your dealing with wolves or Cougars . You can get by with a bead sight if you need to. Also, your gonna want to get something that goes on the gun to hold more ammo. IE a butt cuff or a side saddle. I dont like the slings that hold shotshells because you will find that when shooting that is alot of weight swingin around underneath the gun.
However, if you really want a rifle I can think of two options you may want to go with depending on your budget.
Large Budget- Go with the AR. The ergonmics are great and with a little training it is very easy to run one. However in your situation I would not stick with the 5.56 caliber. A .458 socom should handle a bear nicely but you lose capacity and the rounds are pretty pricey. A good compromise would maybe to go with a 6.8. More power then 5.56 but still hase all the capacity you'll need. Again though, rounds are goin to be a lil expensive and you will most likely have to order them offline. However if I were in your shoes I would look at it as Its my life and I would be willing to spend a little more on ammo. However If you really want to keep your ammo costs down you can find 7.62x39 AR's. So you'll have better accuracy then the AK but still have the same power. Dont get confused though, 7.62x39 is not a bullseye caliber. It is in fact comparable to a 30-30 in both power and accuracy. However you could get another upper in 5.56 and be able to train with either round and target shoot with the 5.56 upper. Just some thought there.
Low Budget- Get a lever gun. If you dont have brown bears in your area then a 30-30 should be fine. If I was living someplace inhabited by brown bears though I would at the very least go up to a .35Rem. Preferably I would be looking at 45-70's or .444Marlins.
Those are what I would consider if I was in your situation. If you absolutely want either a 5.56 AR or a AK then I would honestly prolly go with the AR. I would load it with 62Grain FMJ's for penetration. Why, because the ergonomics are better on a AR, they are easier to shoot fast, and they are more accurate. Whatever option you decide on just remeber one thing. TRAIN TRAIN TRAIN TRAIN and have fun. Best of luck to you in whatever you decide.