Crossing from St Mary's isn't very scenic. That part of Alberta is much like Eastern Montana, basically flat plains.
The drive from Calgary into eastern Banff is amazing however. If I'm not mistaken that's the parks main and most grand entrance. Your highway winds around getting closer to the park and the Canadian Rockies just grow and grow.
Radium hot springs is a big swimming pool with a fancy name, nothing to get excited about unfortunately.
The western side of Banff (and Montana) is much more mountainous. As I recall some impressive grades winding through smaller towns. I drove this route coming south, so most of the grades were downhill for me.
If you have time to do both, it won't be disappointing. Driving from Banff to Lake Louise is HIGHLY recommended. Lake Louise and her sister Lake Moraine are two of the most picturesque lakes in the world.
You shouldn't have any trouble visiting in September. I wouldn't visit in the spring, there will be lots of snow and all the lakes will be frozen. Glacier's signature Going to the Sun road isn't even open until July.
This area is one you kinda have to visit during tourist season, and it's worth it.