I have been collecting the tiny little Wilkin and Sons jam jars you get in some cafés, I can fit 3 in my ultrasonic cleaner and it means I can have a different fluid in each one if I wish.
The brass fine mesh balls are useful sometimes as well for the really small bits.
Like Bob and George I clean just about everything bar the dial and pointers. The only thing I would say is dont use any solvent cleaner type substance that could dissolve the shellac/glue holding the jewels in place.
Since seeing Mark do it, I have started putting the balance back on the plate and it seems to be perfectly ok that way, it does not take long plus the plate gets a clean as well.
Cheers,
Vic