Hello, Castrol CL, is good for exposed bearings, as it will not wash off, as most grease does. It is formulated to work under water.
Found to be very good in RFM bearing, and head stock, I use it for everything
except wheel bearings.
As most machines are now running stainless steel fork spindles and eccentrics,I would be inclined to use either a moly grease or a fully synthetic grease, to prevent the spindles picking up. A general purpose grease is o.k for all the other places.
Of course if you want your spindles to last for ever, you could always fit nylon bushes in your forks.