Jul 30, 2015 - 7:33 AM
Thanks for joining MySwissAlps, Janette, and welcome to the forum!
The route via Göschenen and Andermatt is definitely beautiful. Andermatt-Zermatt is part of the Glacier Express route, but you don't have to get on a Glacier Express train: regional trains are available on this route too, and not just from Brig to Zermatt. You can consult the timetable for details.
No matter which train you pick, the leg Göschenen-Andermatt-Zermatt won't be for free with your Eurail Select Pass, but discounted by 25%. You will avoid Glacier Express seat reservation fees if you choose a regional train though.
Seat reservations for other trains than the Glacier Express are not required, and for some legs not even possible. If you do want to travel by Glacier Express, it's recommend to book seats as early as possible. In any case, you will need 25% discounted tickets for the leg Göschenen-Zermatt, and it won't be a problem getting them. Just go to a ticket counter at the Lucerne railway station, show your Eurail Select Pass and explain how you want to travel.
There is a scenic alternative that's covered up to Brig by your Eurail Select Pass: first, get on the Golden Pass train from Lucerne to Interlaken or Spiez. Then change to the Lötschberg RegioExpress to Brig (enter 'Goppenstein' as a via-station in the timetable to see this connection), and move on with the regional train from Brig to Zermatt. You'll still need 25% discounted tickets for this last leg.