We were there during September two years ago and I rented skis/boots at a shop right next to the base station of the two lifts (one is a gondola and the other is a cable car/aerial tram) that go up out of the south end of the town of Zermatt up to Furi.
The name of the shop was Dorsaz Sport
and it was very, very well stocked with high-end skis and boots for rent. Also, the shop guys were knowledgeable and helpful. BEST OF ALL - when they set up my boots in the bindings, they just asked what DIN setting I wanted and set them to it. No questions about age/weight/ability and chart consulting - they just set 'em to 10 and handed them to me. I liked that.
Here's their location if you can figure it out from this map:
Good luck and have fun. I'm enormously jealous.