Bowing won't be an issue with a game cabinet because the cabinet is structurally rigid. Is that what your concern is?
I use a lot of laminate on many games, and I use both types, the thicker type and the vertical grade. It just depends on the application, and if the extra thickness will be an issue or not.
I wouldn't use a patterned type, ever. That sounds like a great way to make a video game look like a cheap countertop, or worse, one of those horrible contact paper covered MAME cabinets. Go with a solid color.
For black, I use the Matte finish, however it does show fingerprints pretty easily. That has only been an issue on one cabinet, and all it takes is some Windex to remove it (I Windex the glass on my games routinely anyway).
Wade