11811 and Obidiah gave a lot of good information, so be sure to thoroughly read their replies.
The Deore componentry group from Shimano (http://www.shimano.com) is a good choice if you don’t intend to be doing much rough riding, and it’s reasonably cheap to replace. Though it costs slightly more than the Alivio or Asus groups, it will also last longer and be more reliable.
One thing above all: Do -NOT- buy from department stores. Not only are their bikes made from poor quality material and components, you will be hardpressed to get any aftersale service. Chances are, you’ll eventually need something done to the bike (under warranty or otherwise), and even if you can convince the store to help, it’ll take ridiculously long periods of time for the repairs to be made. I have a riding buddy who waited three months to get his bike back from Canadian Tire when he needed work done on it. Spend the extra cash to get a bike from a local bike shop (LBS), and it’ll be far more worthwhile for you.
I think one of the biggest factors in bike selection is where you plan to be riding. If your preferred trails are paved or dirt without many bumps, then no suspension might be needed. However, it will make your rides -much- more comfortable on any surface to at least have suspension on the front of the bike. Chances are that for the riding you describe, a “hardtail,” meaning suspension only in the front of the bike, will be sufficient. Because you’re not paying for rear suspension, the componentry you get on a $1000 hardtail will be better than on an $1000 full suspension bike. A full suspension bike, on the other hand, will do more to keep your rear wheel glued to the trail and your ride even more comfortable. But unless you purchase a well-designed FS bike, you might end up with a sub par rear suspension system that will sap the energy out of each pedal stroke. My personal bike of choice is a full suspension, but I rode a rigid (no suspension) bike for many, many years.
I recommend borrowing a bike from a friend to see if you like the sport before sinking lots of money into it. Far too often I see people spending thousands of dollars on a bike that sits in their garage 95% of the time. From there, ask about a reputable LBS (qualities to look for are good customer service, a knowledgeable sales staff, a well-trained mechanic [hey, you’ll be riding something s/he puts together, so it’s best to have it assembled properly], and a history of fair pricing), and go in to talk to them. I know that Calgary has a massive mountain biking scene (and one I would love to visit!), and that there’s many great shops that can help you. Bow Cycle comes to mind (http://www.bowcycle.com/bowcycle/bowsports/page2/) as one of the stores I’ve heard much about.
Talk to them and tell them what you’re looking to do. Be sure to check multiple stores, because not everybody stocks all brands, and you might find a better deal elsewhere. It’s best not to order off the internet (especially for your first bike), because you want to have a chance to try it out in the parking lot first. Oh yes, if they DON’T let you try it out first, be weary. Nobody should spend that much money on something they can’t test drive first.
If, after borrowing a bike and finding you really enjoy the sport, consider that getting a bike designed solely to suit your needs at the moment might not be the wisest investment. Getting a bike that will be solid enough to allow you to explore tougher terrain later on might be more expensive, but it’ll save you the large cost of having to buy one later. This is not to say you have to spend $5000+ on a downhill bike (essentially a dirtbike without the engine), just enough to get a machine that won’t break apart if and when you decide to tackle a steep, rocky trail or whatever suits your fancy.
Some bike companies that will likely serve your needs would be Giant (http://www.giantbicycles.com), Specialized (http://www.specialized.com), Rocky Mountain (http://www.bikes.com), Trek (http://www.trekbikes.com), Gary Fisher (http://www.fisherbikes.com), or Cannondale (http://www.cannondale.com).
Be sure to check out http://www.pinkbike.com, especially their XC Racing forum. They’re a large mountain biking site based out of Calgary, and you can likely find an awful lot of information there.
Hope this’ll be of some help.