Fuji F10 again.......
You really only need to change WB under tricky artificial lighting. Often
auto WB will get it right. If not you can remove colour casts using software.
There really isn't much light around in artificial light situations so even at
ISO 800 the shutter speed will be slow with a risk of handshake. However
if you take 2 or 3 shots often one of them will turn out ok even at slow
speeds that in theory you shouldn't be able to hand hold. Look at the
indicators on the lcd. If you half press the shutter it shows you what shutter
speed you will get.
However I agree that ISO 1600 is too noisy except perhaps for small prints
so I would rather take a chance hand holding at ISO 800. Of course you
can always use a tripod or the flash. For photos of static scenes then you
can do much better with a tripod or wall and setting ISO between 80 - 400.
Again using manual mode and setting exposure compensation of -1/3 or
-2/3 gives better results.