I am considering taking my Super Speed Graphic to Arizona and Utah for some landscape photography this winter -- mostly flat, some mountains in the background --
Any hints/ suggestions? Specifically, what can I expect from the limited movements? I will be using the standard Rodesntock Optar 135mm lens.

For the most part all you need is rise and the the Super will do very well. The only negative about the Super line is the lack of linked rails for wide angle lenses (90 and shorter) beyond that its a very nice camera.

The type of scenes you describe can be done very nicely with no movements at all. Do some brushing up on hyperfocal distance and how to use it. There are charts on the web that can tell you approximate focus for a given aperture. When in doubt, if you focus at about 30 feet and stop down to f:16 or smaller, everything in a broad landscape should be in acceptable focus. Have fun on yur trip!

You might keep in mind, too, that the 135mm. "Optar" produces an image circle that's not much bigger than the diagonal of the film. For this reason, front movements may not produce satisfactory results when the lens is focused at or near infinity -- which reinforces the previous recommendation that you concentrate on composing your scenes without worrying overmuch about moving the front!

I took an Anny Speed to Wyoming and the Dakotas this summer; I found that K2 and Wratten 25 filters come in handy.
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TR is right in there's not a whole lot of image circle there to play with, but I've never been much for forground-heavy pictures, that are soft close-up. But by adding some rise, you'll crop out the fore-ground that won't be in focus anyway and add blue sky and puffy clouds, things that are real hard to tell when they are slightly soft.

The advice you are getting on the movements is good. I use a Pacemaker Speed Graphic and I shoot mostly landscapes. I don't use many movements with this camera but I do use it hand-held a lot. Use the movements for specific pictures where you have the time to set up. But don't forget to be prepared to use the camera hand held, that's still one of the benefits of using a Graphic. Sometimes there is no time to capture a natural phenomenon with a view camera but there is usually just enough time to do it with a Graphic. Just remember to hold steady.

Have fun.