In a few weeks I will need to drive from Billings to Great Falls. Any suggestions on which route is the quickest one to take and/or which route(s) to avoid?

The shortest would be MT-3 to US-12 to US-191 to US-87. It's been awhile since I drove that route but I enjoyed it (I always prefer side roads if I have the time). An alternative would be to take US-12 into Helena then north on I-15. If the weather is bad, I-90 to I-15 would be less likely to have severe weather delays and might be about as fast.

MT 3 all the way from Billings to Great Falls is the shortest and quickest and, unlike the I90 and I15 alternative, it doesn't have any mountain passes. It's about 220 miles via MT 3 which is a good two lane road with only 2 stop signs on the entire route. Weather permitting, you should be able to make the drive in a little over 3 hours and you'll probably see 100 other vehicles the entire trip. The I90/US12/I15 alternative would be much more scenic, however, with more services.

Thanks. I will be there when there is not much danger of snow, so that will be plus when selecting the route.
The Montana 3 route runs along with some US routes, and it looks like it will not have much to hold me up.