Welcome to climbing, Wes. Glad you're liking it. You'll no doubt get lots more advice here, as well as a little abuse (it is an internet forum, after all). I'll get it rolling with a few responses to your questions:
1. Honestly, I wouldn't worry as much about "training exercises" for climbing outdoors versus indoors as I would about learning skills. In general, train for climbing by climbing, indoors if you have to, but outdoors whenever you can. If you're looking for things you can do at home, then focus on cardio and power in the core and legs-- outdoors, you have to hike to the rocks, sometimes far and uphill and at altitude, while carrying a pack that has more in it than just your shoes and a Red Bull. Once you're on the rock, you must conserve your forearms and learn to climb with your weight on your feet. Learn to climb smart, not just strong. If you're training at a gym, try climbing easy routes without your hands at all, or just using a finger lightly on each hold to keep your balance when transitioning from foot to foot. Or try "silent feet" exercises, in which you focus on the precision of your footwork by trying to make as little noise as possible when you step onto each hold (this forces you to be accurate and controlled and will make you more efficient). Start becoming especially aware of your balance and the direction your body weight is pulling and what that does to your limbs (which you are able to move, and how far away from the center of your gravity you can put a foot or hand and have it be useful, etc. Outdoors, you often must pull sideways, upward, or even in opposing directions to make use of the hold available. In this regard, you'll simply have to spend some time trying different bits of rock to start to develop an intuitive sense of how best to move up on a particular spot. Many indoor routes simply involve pulling straight downward on all holds, and difficulty is increased simply by making the holds smaller. Outdoors, even "easy" climbs can involve laybacking or sidepulling or frictioning for the entire length, with no standard "positive" holds anywhere. You'll need to learn to get creative. The thing that often shuts down first-time-outdoor climbers, especially if they have already tried climbing hard grades indoors and expect to be able to do so outdoors, is learning to "read" the rock. The only way I know to "train" for this aspect of climbing outdoors is to touch stone a lot, ideally by climbing. Even easy scrambling on 3rd and 4th class rock gives you some practice with this, but you can also do it safely close to the ground by trying little "mini bouldering" sessions, where you work on easy (very easy by bouldering standards-- under vertical, or at vertical, or just over vertical) routes and don't go more than a move or two off the ground. You can traverse, or just try getting yourself off the ground and onto your feet and hands and standing there for a moment, doing this on as many places as you can see around you to try. Makes for an odd hike, but it's a serviceable form of practice when you're just starting out and don't have enough safe partners yet to get on a rope with.
But more than anything else, focus on learning the skills to keep you safe. You know how to belay by now, but only in a controlled setting. Now learn to do it with either hand, with a half dozen different devices, from above and below a climber, with bulky winter coats on, sitting or standing or leaning, or hanging from an anchor. Even if you stick to sport climbs outside, learn to safely clip and unclip bolts, to orient your quickdraws in anticipation of the direction of movement you'll take above, and learn to set up a toprope from the anchors, or clean a toprope anchor and thread the rope for lowering or rappelling. Learn three different ways to set up an anchor, even if you end up with a favorite method that you use most of the time. Learn to rappel safely. Learn to tie knots in the ends of your rope. Learn to evaluate when you need to anchor the belayer on the ground, as well as when you might want him/her to be unanchored in order to move around in response to different potential falls at different points in the climb. Learn to decide beforehand with your belayer whether you are going to lower or rappel from the top anchors. Learn to not toprope belay with the rope directly through the rings/chains (so you don't wear out the anchors for the rest of us). Learn to communicate with your belayer when you can't see each other from the top anchors, or hear each other in the high wind. Learn to evaluate bolts and know signs of dangerous wear. Learn to pack a wrench, so you can tighten the occasional loose nut (as opposed to simply leaving a post on MP warning others about it, though you should do that, too).
In order to learn those skills, you will need to climb a bunch of routes outdoors, and by doing that you will naturally become better at the actual climbing on rock.
2. What kind of climbing are you interested in doing outside? I assume you already own shoes and a harness (and if not, those are the ones I would not go cheap on-- focus on fit for both, and get the harness and shoes that work for you, regardless of how expensive or cheap they are). If you are sport climbing, you'll eventually need a rope, some quickdraws, and some other locking carabiners and slings of various lengths. But you don't have to own all of it yourself to get started. In fact, in the beginning, since you'll need a partner to go outside on a rope, and you REALLY want that partner to have more experience than you, chances are good your partners can supply the rope and draws. In fact, not investing in a rope right up front is a good way to ensure that you won't be tempted to climb with someone else brand new-- you'll only be able to be on a rope when someone else supplies it. Obviously, ropes don't come with licensing exams. Any jerk can own one, so you can't guarantee that a potential partner knows what they're doing just because he/she owns a rope, but you actually might want some time to figure out what type of rope you like best anyway. In the early years, chances are you are only going to own one rope at a time, so you'll want to get the right one. Err on the side of longer (at least 60 meters, but ideally even 70 these days), even though 50 meter ropes are cheaper and seemingly always on clearance on the gear websites. Too many sport climbs these days are longer than 75 feet, and the extra versatility is worth extra cost and weight. But also already know different ropes have different diameters and sheaths, and these affect how well they work in different belay/rappel devices as well as how they feel (their "hand"). These things also effect how quickly a rope wears out, so spend some time climbing on other people's ropes before you get your own. You'll start to develop your own preferences.
Quickdraws: In my opinion, for most sport climbing, carabiner/quickdraw weight is not a significant factor, unless you are climbing extremely difficult or long or remote routes. Therefore, consider buying basic but solid biners and dogbones rather than the latest ultra-lightweight wiregate draws. You can get 2-3 basic draws for the price of one of the top shelf draws, and for most applications they work just as well. Also, most of the high-end draws these days use dyneema dogbones, even though the cheaper nylon ones offer slightly more shock absorbtion and a very good durability-to-price ratio (but are ever-so-slightly heavier-- hence the preference at the top end for dyneema). Besides, the slings are the part of your quickdraws that will wear out and should be replaced the soonest. Assuming you keep them reasonably clean and they don't get significantly loaded/nicked/otherwise damaged, your biners could function safely for many years. For sport climbing, I am still using many of the same biners I bought 15 years ago, but I have replaced the dogbones several times. This does mean you might be living with some of your climbing gear for a long time, however, so you may not want to go absolute cheapest, if it means getting a less useful item. Here are the features that I think matter for sport climbing carabiners: big enough basket (generally modified "D" shaped), bent gate (or at least easy to clip) bottom biners, and "hookless" noses. Yes, gate flutter is a potential concern, so yes, about half of my draws are wiregates (and all of my full-length draws for trad/alpine/ice climbing are wiregates), but I find when I am only clipping bolts I care more about the smoothness of clipping and unclipping biners from bolt hangers and ropes from biners, and this is where "keylock"-style biners, or other designs that eliminate the notch in the nose of the biner, are truly worth the investment. That said, I haven't upgraded my whole collection (like I said, you may be living with the first hardwear you purchase for a while, unless you make a lot of money).
I'd say that in general, I regret some of the bargain gear I bought when I was starting out, but on the other hand, that stuff got me climbing at a time when I couldn't have afforded to invest in the better stuff. These days, I have upgraded when I can afford to, sometimes to the highest end stuff, but only when I think it is a truly superior product. Like I said, I would never again skimp on shoes (even though it is always tempting, given how many of the less-than-great or overly specialized [and therefore less useful] models end up on 50% off clearance), and I would not buy an uncomfortable/awkward harness just because it was cheaper, though a harness does not have to be $125 to be comfortable and perform well. My current favorite is the entry-level, all-around Black Diamond one- something like $45, and I wouldn't trade it for any other. It just fits, and the features work perfectly for me. Mostly, what has happened over the years is that I have been able to afford to apply the same "don't skimp" standard to more categories of gear, but they still exist in an order of priority for me, and I have climbed most of my routes on gear that was not always "just right" for the climb, and I still lived and had a great time climbing.
3. A solid partner, who you can trust and who is well matched not only to your level but also to your interests in different styles of climbing, is the most valuable asset you can acquire. Cultivate your solid partnerships like the life-altering, meaningful personal relationships they are. But you can also climb safely with a bunch of other people. Just don't go out there with no standards whatsoever and start getting rides from totally random people at the crags-- there are some truly dangerous folks out there who don't know that they don't know what they're doing. They are accidents waiting to happen, and even though there are generally few of them, they look and sound just like the rest of us at first, so you can't tell just by hearing someone say, "oh yeah, I totally know how to do this." unfortunately, some of them have managed to stay alive through dumb luck through a surprising number of years of climbing, so don't assume that someone is safe just because they have climbed for a long time. I have a only a few key partners who I would go to the high mountains and objectively risky routes with, and then at least a few dozen others who have drifted in and out of my climbing sphere over the years. I have met them all over. A few of my best I met out in the hills, a few on this website. I treat new partner experiences like cautious but enthusiastic dating-- I ask a lot of questions, try to hear a lot of stories, quietly observe practices and behaviors (even as I am being scoped out, too), and I don't make assumptions about common practices (in other words, I err on the side of confirming out loud the kinds of little safety routines and common decisions-- like whether to wear a helmet or not for a given route/crag-- that might become more automatic with a long-time partner). And I pick a suitable "first date" (some mellow sport climbing, as opposed to a serious multipitch route with complex logistics). In some ways, I've been out of the new climbing partner "dating pool" too long, so I'll let others weigh in on whether MP or the bulletin board at the gym or somewhere else is the best "singles scene" these days, but in SLC you at least have a climbing scene to plug into, so I bet it won't be long before you have a few folks to go outside with.
Have fun!