The shuttles go right along Banff Avenue and pick up at a number of hotels. There are a couple of ways you can approach this. Since you'll need ski tickets anyway, you should check out the site: http://www.skibig3.com
They will sell you lift tickets that work at all of the three Banff area resorts (Sunshine, Lake Louise, Norquay) and they also will provide quotes for accommodation from a number of Banff hotels.
Another option might be to check in with one of the companies like Inghams that operate package tours. The hotel I spent the most time at last year (Banff Inn) usually had a tour group in at the same time. From my observations it appeared that several of the more inexpensive hotels along Banff Avenue were also being used.
If you have a time share you can arrange an exchange with the Banff Rocky Mountain Resort (I know they do II and I think they are also tied in to RCI). The resort is about 3 klicks out of town along Banff Avenue but they do operate a shuttle from the resort.
How luxurious do you want to go? I just checked my rate sheet from last winter and I was getting reasonable accommodation for about $60 to $75 a night single. Keep in mind that this included a discount for a season's pass (or one from a coupon book available to locals). My requirements are fairly simple (hot tub, wireless Internet, a bar on site or within staggering distance), and I have a lot of choice. The pricier hotels tend to have a few more amenities but the quality of the room may not be that much greater.
What ages are your family? That may make a bit of difference as well. If you have a passle of kids along, then it may make sense to go for one of the chalet resorts on Tunnel Mountain (farther away from the centre of town).
As for the weather, on the hills it will probably range between -3 to -20 Celsius. If this seems a bit cold to you, be somewhat reassured because it is a "dry" cold. The low humidity makes it much more bearable than similar temperatures in Britain. You should be prepared with multiple layers of fleece that can be adjusted to fit the temperature. At around -10 to -15 (typical skiing weather at that point in the year_ my wardrobe usually consists of good ski socks, polypro underwear (bottom), a midweight fleece top, lined ski pants, fleece-lined ski jacket (detachable lining), fleece neck warmer, helmet, and gloves. At -5 I lose the underwear and change to a lighter weight jacket. At -25 I add a second layer of fleece top and bottom and a fleece balaclava under the helmet (retaining the neckwarmer) and use a heavy weight pair of gloves. Banff is a pretty informal place so the priority should be on packing the clothes you need to be safe on the hill.
Drinking age is 18 and the underaged cannot go into pubs/bars. On the other hand restaurants will usually serve a complete menu of beer/wine/liquor so that is not a hardship (although to my mind the absolutely best burger (beef, chicken, bison, or veggie) and minnestrone soup is at Bruno's Bar and Grill and the adults in your party should be sure to check it out).
There are a number of Bears from this area so if you have any questions or want more info do a follow up post.