what is the best platform for graphics design software and why?

It depends on the type of graphics design. If you are only doing still images and don't plan to use excessively high resolution, basically any computer that isn't very cheap will be fine. Most laptops and probably all desktops being manufactured at the moment can handle at least general purpose graphic design.
You'll need a lot of ram (at least 2GB) if you plan to work with very high resolution images. If for some reason you are doing a lot of processing (for example, rendering 3D images), then you will need a fast processor, or have a lot of patience.

In general, I don't think it's much of a concern as long as it's a generally stable computer.

Macs are always good, but very expensive, so (as a mac owner/user) I'm not sure I'd recommend buying one. They're better than PCs, but is that worth paying more than twice as much??

You probably don't want linux because for graphic design name brand software like Photoshop is popular and probably the best approach.

If you do plan to use 3D software that will require a lot more, and even more if you plan to work with video (or graphics for video).

Generally speaking, Adobe has the top of the line graphics programs (including video), except for 3D, and for that you'd want to look at Autodesk (3ds MAX, Maya, etc), Lightwave, and perhaps Vue for environments. Blender is a great alternative because it's free.