New or other wise, I use gun cleaning solvent to remove any lube or film, and then I rinse them out with denatured alcohol, acetone, or brake cleaner. I don't lube them at all. A long time ago I lived where the humidity was extreme and noticed surface rust developing between reloading sessions. I decided to give them a light coat of mineral oil, since it isn't a penetrating oil, it has a thin consistency, won't build up or dry out, and it is very easy to remove with a denatured alcohol or acetone soaked patch, or even plain soap and water. But I don't like to expose my dies to water either, just saying it will wash out easily.
I've read that some reloader's will use vegetable oil. But my experience with vegetable oil is not good. It dry's out and gets hard as a rock in as little as just a couple of days, and then it is a pain to remove.
I've used brake cleaner before, but it isn't any more effective than acetone or denatured alcohol, and costs more to use because it usually comes in an aresol can. But any one of the three are good because they are non residual, will rinse away anything, and they all dry instantly.
FYI, if you go with acetone, make sure it is pure acetone and not finger nail polish remover, because will usually have other stuff in it.