The LCD on the back can be cleaned with just about any brand of optical cleaner. I use the Kalt brand, but I believe its really only Alcohol.
You also need to determine if you are cleaning the actual LCD surface or a plastic cover. On most of the LCD's I have used, Kodak 660, 560, Canon 1ds, all have a plastic cover over the LCD. So this surface is not glass and thus can create a bigger issue, scratching as all plastic will. Make sure your cleaning device is free of all dirt and I will usually either blow off the surface or brush it with a small brush first.
The reason I don't want to scratch the plastic is that you can basically never get it out and it will effect the view of the image. I have also found that the best cleaning material is a piece of chamios leather that I found in a camera store. Very soft.
If your camera is a D1x or D1, there not only a plastic cover but a anti-reflective coating. This adds yet another issue has if you aren't careful you will remove the anti-reflective coating. I did this on my first D1 and had to have the entire LCD and cover replaced as you really couldn't view the image due to all the streaks.
The last thing to consider is a simple cover material. I use a clear thin plastic strip, meant to cover a Palm display. I cut it down to size then just lay it on top of the plastic cover. ARound once a month I have to replace it, but this keeps all the scratches and such off. It also allows you to pretty much wipe the surface with anything.
I noticed now that the Hoodmanusa company sells these also, but they are precut to the various camera LCD's. www.hoodmanusa.com
Paul