Just did this a couple of months back but we were travelling by land yacht a.k.a RV/motorhome. It's sort of home for us (we just never get out to that part of the world often living insularly on the coast) so we won't do the same stuff as a 1st timer would.
Check the O/W car rentals first. Said to be cheaper in one direction than the other. If you can book through Canadian Affair, it'll be better (includes insurance and lower rates due to matching O/W rentals or some such). I would say easier to fly one way, and some say to just do a round-trip out of YYC and skip the rest. Drive from Vancouver to Banff can be done in a _long_ day, not that I would do it. If it's Jasper/Banff/Calgary, Rocky Mountains you want to see, I'd just go from there instead of via Vancouver (unless it's just a change of flights). You want to drive between Lake Louise and Jasper in both directions and dedicate a day to each direction. Add 2 days in Jasper, and at least 1 day each in Lake Louise and Banff (if not more) so you're up to a week already. Hope you have a healthy budget as accommodation is hideously expensive; lowest grade room at Emerald Lake Lodge in Yoho NP was $800/nt in mid June, and the Fairmonts in Lake Louise and Jasper were something more astronomical (my wife checked for kicks). Cheaper hotels are not cheaper by much. Even home stays in Jasper (not much accommodation compared to Banff) are $300 a nt. Even with gas at C$1.70-2.20 / litre then, and the land yacht getting just over 3 Km / l, our 4,200 Km trip was reasonable due to accommodation prices.
Just note that there is ongoing road construction (highway bridge being built on a steep and unstable mountainside) just east of Golden which has required complete road closures for almost a month over the past few years. Some stretches of highway leading to/from Vancouver were destroyed late last year by floods and a few are still being rebuilt (causes delays during busy travel periods of which there should be non unless in late June), and may well experience such flooding again.