BeeVee -
You don't give us much info to work with. Would you be flying in/out from a Canadian city, the U.S., abroad?
Where, exactly, will you be riding to/from - the entire ACA route?
You mention limited touring experience, but how strong of a cyclists are you and others?
Southbound or northbound?
I've ridden the Northern/Canadian Rockies many times - both east side and west.
There uses to be a forest road border crossing on the west side of Glacier NP that is now closed.
So, there are lots of options out there that you might combine.
Are you willing to do any dirt?
Starting point and ending point - -
Jasper has a delightful little train station with VIA Rail and bus service. Very convenient.
Missoula no longer has train service and buses in the U.S. can be from hell.
Missoula has limited air service - will require a couple of transfers.
That said, it is probably safer to ship your bike to a bike shop.
In 30 years, I've had airlines goof twice and Amtrak goof once.
I have never had a problem shipping.
(And with airline fees - shipping is probably cheaper.)
Panniers and trailers each have their advocates - neither option is cheap.
But panniers are easier to ship - airlines will nick you for the trailer.
Airlines have hefty bike and excess baggage fees - and will count each pannier.
Some people use a cheap sports bag, I use a box to combine all things.
(The compression straps I use for my gear - I use thru the box corners as handles.)
Amtrak/VIA have much broader/cheaper baggage allowances.
I have always toured with panniers.
One reason is because I do dirt segments - maybe 10%-15% dirt.
That allows me many more route options.
As for the route -
South of Glacier NP, the east side (US 89) is more scenic and has less traffic than the west side (MT 83).
Going to the Sun has fewer bike closures westbound, but is also more scenic - the the morning sun illuminating the peaks.
Since you can't cross the border on the west side, you need to go via Waterton NP.
I find Hwy 95 from near Fernie to Radium rather meh. More traffic and medium scenery.
There are two options - eastside, Hwy 22 from Lundbreck to Longview, then Highwood Road to Kananaskis
Or BC 43 north from Sparwood to Elk Lakes and over Elk Pass on dirt telephone road to Kananaskis.
(Kananaskis is spectacular - the preferred playground for folks from Calgary.)
For both options you can take the paved highway into Canmore -
Or you can take the unpaved but good quality Spray Lakes Road!!
You can hit the finest parts of Kootenay NP and Yoho NP by cutting over the passes from Banff.
Three weeks minimum - esp. if you include travel time.
I would allow for an extra day at the end of the trip in case of bad weather, mech troubles.
That way you are not jonesing at the end of your ride trying to get there.
And, yes, hiking is a great part of this trip.
You should seriously consider a side trip to Many Glacier area in Glacier NP - fine hiking.
The Canadian national parks have old fire roads where bikes are permitted.
(These make the dirt roads I have mentioned look like picnics, but they are worth it.)
You can ride deep into the parks and camp in spectacular locations.
If you are flexible on the route, I would be glad to make a few suggestions.
Journal of much longer trip -
https://www.cycleblaze.com/journals/wna2005/Start on Day 52
Photo - Going to the Sun Road, Westbound