mid-November is usually when the snow begins to stick around for the rest of the winter in Edmonton. We don't get a ton of snow (130 cm per year), and it is spread out over about 6 months, so the roads will probably be fine, though there is a chance of running into a snowstorm and crappy driving. That's about the best I can tell you.
You can fly from Calgary to Edmonton in about 30 minutes, though with all the waiting at the airport before your flight, and then collecting your bags after your flights, driving probably ends up being faster (3 hours).
+1 to Cbaarch's suggestionmof the Road Arrow. This is a luxury commuter bus; let a professional driver deal with any potential problems.
It's an easy drive, in that it is straight down the highway, BUT it's very busy, and the weather as mentioned could be dicey - or not - totally unpredictable. I like the Red Arrow, and it is my own preferred travel method between the cities, but I would say whether it's right for you depends a bit on what your plans are in Edmonton, and where you are heading afterward.
Other bus options between Calgary and Edmonton are the Ebus (operated by Red Arrow), and Greyhound. I would not recommend Greyhound as Edmonton's stop is at an inconvenient location for most travelers. Red Arrow's stop is right downtown (and one on the south side of the city as well).
I have memories of Remembrance Day ( November 11), standing at the cenotaph with it beautifully clear, cold -26, and about a foot of snow.
When travelling into the mountains during the fall/winter season, it is strongly recommended to rent a vehicle that has all wheel drive. Depending on how many are travelling with you and luggage, a SUV vehicle should provide the traction and stability you may need. Leaving Calgary and visiting Banff and Lake Louise, you will be on highway 93 after visiting Lake Louise. One of the most beautiful highways in Canada is highway 93 between Banff and Jasper, so I would make that the number one option to travel upon going to Edmonton. Once you arrive in Jasper, you can take the Yellowhead Highway, highway 16 to Edmonton. But as you travel in Banff and Lake Louise, you should search for the highway conditions and weather reports for the Lake Louise/Jasper trip. You will be travelling over high passes and the snow and visibility may be a challenge for you. I have travelled that route many times and even in the middle of the winter. The viewpoints on a clear sunny day are breathtaking. Please ensure you make reservations ahead of time for overnight accommodations. Ski season opens in early/mid November and weekends for sure will prove to be a challenge to get a room.
As a further option going to Edmonton after visiting Lake Louise, (if the weather is bad or you don't want to travel further in the mountains) you could leave highway 93 at Saskatchewan River Crossing, and head east on highway 11 to Rocky Mountain House and on to Red Deer. You then can pick up highway 2 heading north to take you to Edmonton.
In all cases, be aware of the road conditions and weather reports as you travel. Weather changes very quickly in the mountains. Enjoy your trip, you will be seeing many beautiful places.
There's no need to get a AWD or 4WD drive for any other roads around here. Nor an SUV. What you need is snow tires and good, solid winter driving experience. AWD/4WD and a bigger vehicle will just give you all illusion of safety -- won't do any good in helping you to deal with a slippery road. 4WD drive just becomes 4 wheel slide. If the conditions are so bad that you can't deal in a regular sedan with snow tires, you shouldn't be on the road.
I think we'd also not suggest driving between Jasper and Lake Louise in mid to late November unless you have plenty of winter driving experience and flexibility in your schedule. The problem is that road conditions could be just fine, but you could also encounter really bad conditions. In November, there will be no hotels/stores/anything open along the parkway, and there's cell reception. So if something happens, it can be a long wait for help It's one thing if you have comfort in driving in such conditions, are in your own vehicle that you know and know how it handles & has snow tires and have flexibility to cancel or reschedule a trip if things go south. But in a strange car, in a place you don't know when you need to get somewhere, not a good idea.
As mentioned above, I think your best bet is to focus on Banff/Lake Louise. If you have no specific reason to be in Edmonton (family, friends, meeting etc), and can fly to Calgary, I'd do so. Otherwise, take a bus or rental car and drive via Hwy 2 to Calgary/Canmore/Banff. From the airport or Edmonton it's no farther, and sometimes faster to Canmore, for instance, than to Jasper.
Then base yourself out of somewhere in Lake Louise, Banff or Canmore. That gives you the option of doing a part drive of the parkway if the conditions are good. The stretch up to Peyto Lake is very scenic and they're pretty good about keeping that stretch in decent condition as long as the weather cooperates. That approach also gives you flexibility to choose the best weather day, rather than be fixed into a day you have to drive south.
I would not worry about accommodation in November. That's really early in the ski season, so even weekends are not at all crowded. Most folks, particularly in Lake Louise/Banff/Canmore will be doing day trips from Calgary. And in Jasper, even a crowded day in Marmot isn't going to come anywhere near filling hotels and PHAs. The only exception might be the last weekend of November in Lake Louise when they have the World Cup alpine ski races. But even then,