How much time will you be spending in the area? How much walking/hiking are you interested in?
If you have the time, I would encourage you to consider renting a vehicle and doing a loop from Calgary to at least Lake Louise, and if you have a few extra days, extend your journey all the way to Field and Golden (Golden is about 2 1/2 hours from Calgary, just for reference.)
Banff is beautiful, but is known as a giant outdoor shopping mall, where bus tours drop off hoards of people to shop/gawk, then load them up and carry on. Definitely stop in and check out the beauty, but if you want to really experience the Rockies, I would suggest carrying on to the Lake Louise area and doing some of the amazing walks/hikes (especially one of the Teahouses - Plain of 6 Glaciers is my favorite.)
From there, plan on a night or two in Field, BC - a tiny little town just across the BC border. Most of the accommodation options are in Heritage homes, and you will be less than a 15 minute drive to Emerald Lake (DON'T miss this) and Takkakaw Falls. There is also an amazing restaurant there called the Truffle Pigs Bistro.
If you carry on 45 minutes further down the road to Golden, you will have plenty of options for activities: Skydive or tandem paraglide off Mount 7, float down the Columbia with wetlands adventures, whitewater rafting, check out the wolves at the Northern Lights wolf center, or simply enjoy the farmer's markets, galleries, and live music in the square. Irrespective of all the activities, driving Highway 1 from Calgary to Golden is scenic all on its own!
If you have specific questions, feel free to PM me (as I am beginning to sound like a giant advertisement.)
In response to your money question - credit cards are widely accepted, they will gladly take your US cash but hose you on the exchange, and it never hurts to keep some cash in your pocket for fresh fruit at a roadside stand, or some jewellery or fresh baking from a local artisan (though many will run your card on their smartphones now!) :)