32mm is probably enough. I know a guy who used to lead tours on the Mickelson, and he said 35mm was enough for everything. There are some loose sections, and some with large gravel, so I use 38mm tires. Most of the trail is railroad grade, although there is one very steep hill near Deadwood (click on "3" on the link given by colorado dale). It can be bypassed by going up around Sugar Loaf on the way south, which is worth it for the views anyway.