Not an expert here but I've avoided watch-specific oils because many have expiration dates, and it seemed to me that the sorts of forces encountered in a shutter might be more comparable to those found in clocks, not watches. I wound up with Neoval Rubin G8, an inexpensive general-purpose oil, and in fact, Esslinger once sold it as a clock oil. To apply, I use a yellow Bergeon 30102 "Very Large" size applicator which is a decent size for camera work.
Grease: I use Molykote-G paste on slow moving mechanisms, mostly metal-to-metal contact areas where there may be potential for higher forces, such as the shutter speed ring. It appears very similar to gray factory paste found in many cameras. Not expensive, and a tube lasts a very long time.
Just finished working on a Seiko SLV and this combo of lubes worked very well except for the self-timer which I suspect was designed to be run dry, because it runs great that way, but stalls if attempt to oil it, particularly the faster-moving parts where torque is very low.