So for the Matterhorn I’d definitely recommend one of several new-generation hybrid boots that combine the attributes of leather AND plastic boots. La Sportiva's Nepal boots ($475) are great. They have tough 3.2mm leather uppers that are treated for waterproofness, along with thick rubber rands around and above the sole to protect the boot and keep out snow or water. Insulation keeps your feet warm in cold conditions. They take crampons well, and with the leather, you have better "boot feel" for rock work.
There are other good choices. Lowa makes a boot called the Silberhorn GTX ($440). Very similar to the Nepals, with leather uppers, Gore-Tex liner, insulation, and nylon shank for stiffness. Or there is the Asolo Makalu GVs ($380). These aren’t quite as warm as the Nepals or the Silberhorns, but they have a very close-to-the-foot design that makes them more like super-warm rock shoes than "mountaineering" boots. Very sleek. And they work great with step-in crampons.
Try a few different boots. Any of these above will work, so get what fits best. Then you’ll be happiest.
Have a great climb! And send us a picture.