Derek:
I was taught to use vegetable oil, but it goes rancid in a few weeks, so I have been using 5w synthetic motor oil for a long time now. The same oil pot is good for both lubing and rust-proofing tools, and the oil never hardens or goes bad. Mobile 1 has the best smell, IMO.
Mineral oil works very well too. I used to use Olde English lemon furniture polish, which is just light mineral oil with scent, but motor oil is cheaper and sticks to the tools better. I would avoid anything with silicon in it.
I use this same motor oil to lube the soles of my wooden planes too. At first I was concerned that a petroleum product might weaken, soften, or damage the wood, but it has not harmed them at all.
Perfect for saw blades, of course.
Stan