Do we need to get a reservation in advance or just show up at the train station? This will be in September. What about room for luggage on the train?
Just show up and board the train. There will be racks for large luggage at the entryway of the train car, plus overhead racks for carry-on and smaller size. You will change trains at Visp.
Yep, just did this a few days ago, and easy-peasy. The ride from Visp to Zermatt is especially beautiful if you have a clear day. Fingers crossed!