As i said this is one of my favorite places in the world...not trying to be a smart ass miniross, but being from the area, i thought i would help on the geography issues....
Sunshine is only 20k away but by the time you ride up the gondola, you are right, it is close to an hour. Sunshine is always open to may 20th or so, so you don't have to worry bout snow in march. Panorama is in British Columbia which is about 2-2.5 hours away from Banff. Jasper is in the other direction north of Banff and is phenomenal...if you go there you will love it.
A moose is always good to see, more than likely you will see elk though in town. We call cougars Milfs now...plenty of those around!
Go here for web cams of sunshine
As far as Norquay goes, it is the closest to Banff(a couple of minutes) and tend to cater to locals. However, I have had some of my best days there. There is a lot of expert terrain there if you are into that.
I am going to big white tomorrow... a long way from Banff, and on Sunday to Lake Louise where my boy is competing. You will Like the area.