Awesome! Post pictures - always loved those.
M1 0w-40 is a great oil for that car. You could also consider pennzoil platinum euro 5w-40, as well as the HDEO 5w-40 oils. That is not an engine that needs a crazy 60wt as I recall.
I really am a fan of the Amsoil manual transmission fluid for BMW gearboxes. While many claim that redline is the way to go, I always found that the amsoil fluid held great shifting characteristics longer.
Im not sure there's really a best diff fluid, but if you have an LSD, Castrol XJ, which is a 75w-140 LSD lube is the right stuff. Im not sure there's a real issue with going 75w-90 in that car, you might consider 75w-110 though if youll be driving it hard. Amsoil SVG is my favorite.
Also get some G-48 blue coolant and do a flush of the radiator at minimum. Make sure there's no plastic parts in there that need to be replaced (water pump impellers, etc).
Pictures!!