Best way to get to Banff from Vancouver is to fly to Calgary, then either coach or rent a car and drive to Banff. There are no regular scheduled passenger trains from Vancouver to Banff (not even the Rocky Mountaineer, which is just a tour train, runs that time of year). Driving probably isn't an option, as it's roughly an 11-hour drive from Vancouver to Banff, assuming perfect road conditions.
There are lots of good hotels in Banff; you'd be travelling in shoulder season, so there should be good deals just about anywhere you look. The Fairmont Banff Springs is probably the most prestigious hotel there, but it's pretty po-faced and can be very expensive, even after deals. The Rimrock is somewhat cheaper, but it's where I'd stay if money were no object (also, the restaurant at the Rimrock is one of the best in Alberta, if not Canada). There are a number of cheaper options out there too; have a look online to find something in your price range.
As for what to do, there's a reason why early October is shoulder season - there isn't all that much to do then. It isn't really nice enough for most summer activities, and the ski hills aren't open yet. You could probably fit everything worth doing at that time (museums in town, hot springs, Sulphur Mountain gondola, trip to Lake Louise) into a couple of days easily.
Time...to un-pimp...ze auto!