A. Davis , Mar 05, 2008; 10:20 a.m.
The approach I would suggest depends a lot on where the walls are located...if you can
bounce off the green wall you might be able to avoid gelling your flash to match
the fluorescent lights, which would be kind of cool, but probably won't work.
I'm guessing that the basement has a low (8-10 foot) drop or white ceiling, so you could bounce your flash off that to diffuse and spread the light.
However you use your flash, you are going to want to drag your shutter and bring in some of the fluorescent light. My typical setting for shooting in a room like that might be ISO 400 1/60 f2.8. Use your camera's light meter to take a reading, then set your camera on manual and dial that setting in, plus or minus a stop or two to adjust for how you want the background to appear.
Not seeing the bright green and bright orange, my gut would be to go with the white wall as a background. Set your exposure and white balance so that the wall will be white, then set your flash to expose the kids. Buy a CTO gel, and your flash color will match the flourescent.