If you want to go to Banff/Jasper and Vancouver, I'd suggest flying to Edmonton, driving to Jasper, then driving the Icefields Parkway (one of the most scenic drives in the world), then driving to Vancouver. The drive from Jasper to Vancouver via Lake Louise is about 12 hours (a 2 day affair for sure), but traveling Jasper to Vancouver by air burns up a whole day anyway and isn't very interesting. The train is also an option but: it's almost always delayed, it's extremely expensive, and in a car you can stop where ever you want and actually walk around, take a photo that isn't through a window, etc. I love long haul train travel, but I wouldn't bother with it in Canada.
Hiking is the main thing to do throughout the region although Banff has quite a few contraptions for seeing the mountains without actually walking anywhere and Jasper is becoming like that too. If you want to see the best scenery and are fit and willing I'd suggest doing some of the longer, harder day hikes off the Icefields Parkway like Wilcox Pass. The Parks Canada websites have abundant details on all of the hiking trails.