Armed_princess, welcome, you initiated a fascinating discussion and lots of good advice. It's one of the most interesting threads I have read since I signed up here almost a year ago. I hope you don't find it too overwhelming. Getting quickly from a pellet gun to a truly lethal weapon is not easy, but is doable if you are determined.
There are a few points that struck me as not being well resolved.
One is what weapon you will carry initially, and after you are more accustomed to firearms.
Since you have the offer, I'd accept the snub-nosed .357 and a holster, and buy a minimum of 200 rounds of .38 special for it to get accustomed to it. Get 1 box of .357 for serious business. At least you will have an effective basis to get started, although it will not be optimal. Make sure you are thoroughly instructed in its operation and get one supervised practice session at a minimum.
I make this suggestion because you need to be armed right away. Waiting for the perfect decision for 6 months leaves you exposed for that time.
If you can afford it, buy an inexpensive .22 revolver & holster of about the same conformation to train with. [Please stay away from semi-automatic pistols (also referred to as autoloaders or pistols): they are too complicated and usually offer less power than a revolver for the same bullet.] Get 1000 rounds of cheap .22 ammo for practice (no more than $20). Plinking at cans is lots of fun, and the kids can join in (maybe the pellet gun for the younger). Being able to hit a soda can at 7-10 yards is plenty of a challenge, and you do not need to train for bulls-eyes for the kind of defensive shooting you need. For serious practice, use a big piece of cardboard, so you know where your misses are going; it's not practice if you don't know what mistake you are making. Add a 3" felt-pen circle to aim at, & try to keep your hits within a 9-12" circle at any range.
Without the kids, practice with the snubbie and .38s: you will probably not become as accurate with it as the .22. However, remember your predator will offer a target of more like 12-18", so just get a bigger can. Try a few .357s when you feel comfortable with it just so you know how they feel. If you have to use it in an incident, your adrenalin rush will will interfere with careful aiming if you have not trained, but it will prevent you from noticing the noise and recoil. However, the recoil will throw a second shot off target if you don't practice re-aiming quickly (and you WILL need a second shot in all probability).
The .22 is NOT sufficient for cougar, and not ideal for human predators, although it may be sufficient to dissuade/disable them in a pinch. Certainly carry it until you can manage the .38/.357. And it's OK to carry .38 rounds until you are ready for the .357s.
The biggest problem for you is whether to carry a revolver or a long gun (rifle or shotgun). No matter what weapon you select, you have to carry it! Long guns are heavy and awkward, and it's easy to be tempted to leave them at home, or put them down while you are working. You also have to be able to hit what you are aiming at, which is usually easier with a long gun. However, as was pointed out, you can be ambushed by a cougar or human predator, and not have the opportunity to deploy a long gun, while you very probably could get a shorter-barreled revolver into play. So there are three different variables to consider, convenience, ability to hit, and ability to bring the gun to bear on a target. A difficult choice.
It is quite difficult to place a revolver shot where you want under stress, even at short range, (without a LOT of practice under stress - as I discovered in a competition). It is also unusual to get a 1 shot stop. Adrenaline keeps predators on the attack until sufficiently disabled. You also need to know where to aim to place your shots effectively. I can't go into that here, but there are two strategies - shoot for vital organs (usually the lower part of the chest cavity where hear and lungs lie - remember, 1 shot may not stop and plan on several), or shoot to "break down" the attacker. That means disable it so it can't advance: a shot that breaks the shoulder or pelvis will likely accomplish this; however just because the predator falls, don't assume too quickly that the fight is yet over. (Head shots are usually too difficult, especially on a moving target, and not always effective).
Remember, I mentioned that it is difficult to place shots with a snubbie even at very close range, especially when you are rushed. The .44 Redhawk is a much better weapon, accurate at longer ranges and more powerful. Like the long guns, it can be more of a "standoff" weapon. After you have mastered the "feel" of the snub, I recommend giving the Redhawk a try. I have shot one; it is a lot of gun, but it is fun to shoot and very accuate to over 50 yds (you did not mention the barrel length, which is an accuracy factor). If you can master the Redhawk, its power and accuracy is plenty of protection at short or long range for any threats you will encounter. (You will need help selecting practice and defensive ammo for it). A friend was telling me of a gun club open day where a lot of weapons were out for people to try. He demoed several revolvers, and then let folk pick one to try. He directed a little ole grandma to a .38, and she shot it with a big smile. Then she pointed to the Redhawk and asked "can I try THAT one?" She fired a few shots with it, put it down, and gave the club member the biggest granma grin he ever saw. I understand how she felt. (Have a Pachmeyer grip fitted to it - much more comfortable to shoot). You can get a sling syle holster for this large revolver (with or without a rain flap), which may be more comfortable that a belt holster.
You will probably do most of your revolver shooting with a 2-handed grip, but you need to be able to shoot one handed in case you are charged, and don't have time to attain a 2-handed grip. The Redhawk may be too heavy for this situation. With a sling style holster holding the .44 in front of your body, you may be able to get two hands on it as fast as one. Another issue is fit (with alll weapons): does the Redhawk fit comfortably in your hand(s). If not, a longer barreled .357 with a smaller grip may be better for you. A suggestion: look for a Smith and Wesson Combat Masterpiece with 6" barrel (used - no longer made; lighter frame, smaller grip).
As for long guns, I think shotguns got a bad rap here, generally. A semi-automatic rifle in about .30 caliber is fine, especially a carbine (a short barreled design, like the M1 someone mentioned; they are not made any more, and are a bit pricey. Place the shots the same way as a revolver. The other choice is a short barreled shotgun: my choice is a Model 500 series Mossberg pump gun in 12 guage because it is a litle over $200; make sure it has an extended magazine holding 7 rounds (some don't). Like a rifle, it points accurately. I'd buy dove and quail shot for practice and familiarization, and 00 Buckshot for serious work. You really need to practice working the pump under stress (get your BF to shoot a few hundred rounds through it to loosen up the action; all new guns need some break-in to smooth them out, and to prove their reliability). A 12g shotgun is a formidable weapon at under 25-30 yards. You can shoot a critter in the face with it and almost certainly disable it with the scatter of shot: at shorter ranges it will blow a big hole in the target. Try it on paper at different ranges.
The problem with a shotgun is its recoil. You will need to have a gunsmith cut down the stock to fit you properly, taking into account addition of a good recoil pad; add a sling. When you shoot, as with other weapons, lean into it a bit, so it won't kick you off balance. I have read that a shotgun is commonly carried as a bear gun in Alaska out in the woods and around the cabin because it is quickly deployed, easy to hit with, and hard-hitting. You could probably for your circumstances go down to 20 guage which has lighter recoil, but NOT .410, which is for the birds.
Make sure you are shown in detail and more than once the operation of each weapon you acquire. Probably you will be able to find a near-by family who will take you under their wing and help you with your weapons. In the mean time you can carry the .22 until you are ready for the .357 and or .44. And you can choose between a revolver or long gun according to the occasion. (If I were taking the long gun I would keep a revolver in the truck or on my person - certainly on my person if I were likely to lay down the long gun while working away from it). I'd certainly plan to own one revolver and one long gun at a minimum.
I agree that black bear don't present a big risk (with the possible exception of humans accidently appearing to threaten mama's cubs). Cougar will silently stalk adults and smaller prey like dogs and children, more often than we know, rarely with tragic results. They will come to the house and take cats off the porch (I know of an instance). But encounters are rare. You have not mentioned feral dogs, but they are a potential danger to be aware of. Last, feral humans. The best house defense weapons are generally considered to be a shotgun and a flashlight (with a dog warning system). Will your BF cooperate in a home defense plan? (Lots of discussion on that subject here).
I hope I have tied up some loose ends usefully. I'm sure there will be some disagreement with me - there are as many opinions as there are THR members. Pick what works for you. You will find animated threads here on all the sub-topics we have mentioned.
You MUST dedicate some regular time for practice: I'd suggest a minimum of 1/2 hr/day. Warm up with the .22, then work with the next larger. You need to progresss to an effective weapon ASAP.
I'm sure you know the 4 rules of gun safety, but as a reminder:
http://www.thefiringline.com/Misc/safetyrules.html
The fifth rule is to execute a plan to keep your weapons safe from your kids, while having the necessary ones accessible to you. Solutions to this problem tend to be very personal.
I envy your retreat to the Cascades, wish you well and stay safe!
AND KEEP ASKING QUESTIONS! There are lots of other issues you will encounter. Post them or PM individuals.
C