A green cast won't be a problem with a correct WB setting - which can remain locked on the camera to be used in that room. And if the lighting will remain constant you can gel your strobes to match as well (read strobist.com . It's when you start playing with mixed ambient lighting that you're going to run into nightmare situations.

Whatever lighting is decided upon, it would be a good idea to have the capability to dial it back so it doesn't contribute to the photograph and instead the photo is lit by your strobes or other purpose-positioned lighting. Overhead lighting alone isn't gong to produce the most flattering images, especially in a room painted black or grey. You're going to get unflattering shadows.

But if you're gong to use the lighting only for when you're setting up equipment, it doesn't really matter what you use as long as it doesn't alter your own perception of what you're looking at. Use something with high CRI if you want to see an accurate representation (with your own eyes) of the garments.