Next I expect to see "Best hacks for shooting my wife on a beech" :-)

You can do research on filmmodes, white balance, and hacks. Then just run some tests with your specific light. There's no one single answer, as you will have to decide what looks good to you.

A more useful thread would be about chroma-keying / green screen & blue screen and the hacks in general (unless one already exists!).

GH2 is still 4:2:0, so its still very limiting in its usefulness. I've played around at 176mb with it.

The 4:2:0 Colorspace can be limiting but at least you don't have to deal with the line skipping artefacts that you get from the Canons. Get your footage as neutral as possible to keep edge artefacts down and as clean as possible (absolutely no sharpening). Banding can be a pain so light your green screen as evenly as you can. Try to stage your talent as far away from the green screen to keep spill to a minimum.
If you can keep the screen slightly out of focus range this will help even out the colour. Of course if your using tracking markers this may not be an option.

Basically the same rules apply wether your using a gh2 or a Red. And believe me. Poorly shot 4k can be just as much of a pain to key as anything else.