in rain i would ride slow and use wet lube for your bike. i degrease and relube the chain and moving parts regularly. if it's going to rain, i use wet lube. if it's dry, dry lube. - also cleaning up the rims/brakes when i can.

as for keeping the rain out of your face any eye wear doesn't really help. a visor is the best thing to help with that - at least for me it is.

with wet handlebars, i usually dry them before i place my hands. then i don't move my hands for the rest of the trip due to them slipping. also for pedals i have toe clips that reduce slippage on pedals and keep them on.

best of luck!