I have ridden from Winnipeg to Vancouver and Calagry/Jasper to Van many times and find the roads to be ok more or less. They have repaved a large portion of Winnipeg west since 2016 which helps.
I was using Gatorskins in 28mm and found them ok but sometimes a bit harsh and now have switched to 32 which I like better. You can run them a bit soft and still not worry about pinches. Less than 28's and I would worry about pinch flats or the harsh buzz I'd get trying to pump them up to avoid them.
The decision as whether to seek puncture protection or not may depend on how much you like or don't like fixing flats. The biggest culprit I have found is small bits of wire from worn out radial tires that like to sneak into the tire. With a support vehicle and extra tires/tubes I would consider less protection and increased performance over high protection.
From Winnipeg west you would want aerodynamic rims if anything as you have vast distances to cover. The prairies aren't really that flat and have many small rollers along the way. Wind direction is a toss up mostly but you will hit head winds definitely past Calgary to the Kicking Horse pass. I don't really know what mountain rims are (for climbing?) but east to west the big hills are all down. West to east you go up more but the climbs are all long and relatively gradual compared to European alpine passes.
Interesting topic as I am considering a fast (ish) trans Canada tour next summer 2020.
Last edited by Happy Feet; 08-23-19 at 10:46 PM.