I am with Dan on this for group shots, my daughters school had a class shot done recently and it was done outside in natural light I have to say though it would have definately had benefited from some sort of fill flash though as all the eyes were a tad shadowy.
They seem to use a two light set up for the individual portraits probably 2 soft boxes looking at the photos.
With regards to a background you would probably want a fairly narrow one to fit in most rooms something like
this should do the job nicely as it will go from 1.4m to 3.8m wide and has good height.
With regards to backgrounds you could go with cloth or muslin but that can be tricky to keep clean and crease free (depending on the material) or the other option is to get paper rolls as these are easy to transport and can be torn off when it gets creased or mucky.
I got my white paper roll from the same people (Creative Backgrounds) that do the light stand, the background support I use is a cheap ebay one that cost me about £50 and it is good enough for what I use it for.
The other option is something like
this