For a frame, I'd look for some stainless or aluminum channel, or angle stock, and have the corners of it welded, ground and polished so it looks like a solid piece. I've never really seen a good looking wood frame for one of these, they all turn out looking homemade. Copper might look nice also, but attaching the corners seamlessly will be more problematic with copper. You could braze the inside of it, and fill the outside gaps with Just for Copper brand Epoxy so they are barely noticeable.
The benefit of brazing is you can buy a MAPP/oxy torch for $40 and do it yourself. Otherwise, you either need to have a welder, or pay someone to do the aluminum or stainless for you.
Like TXFlatLander said, white on the bottom area so it blends in is a good idea. But, if the screen sits back far enough when it folds up, you could just put a white lip that hangs down off the front of the cabinet to hide it also. Angle the ends so it blends in, like an upside-down trapezoid, and countersink the screw holes from the bottom.
You may even be able to design something awesome at emachineshop.com and put that on there.
http://www.emachineshop.com
You download their software, design your part, and hit a button to get pricing and buy it. It arrives in the mail a few days later. Awesome.