A few tips, to ensure your painting stays in perfect condition.
Paintings collect dust like everything else, however they don't really need to be dusted very often at all. If you really need to do so, then I'd recommend that you purchase a very very soft brush, a make-up brush perhaps, and work extremely lightly, particularly on the surface of the piece. They do tend to accumulate dust on the tops, as you would expect.
Silicone release paper (or standard household greaseproof paper) is perfect for wrapping a painting in, as a primary layer when it is to be moved/shipped. Silicone release paper will not adhere to the surface of your painting and so you don't run the risk of its surface getting marked or imprinted. Oil paintings are odd things, because they take so very long to dry and because the painted surface is often shiny, wrappings will sometimes adhere, particularly bubble wrap, which, whilst being great for cushioning things, will adhere to and mark the surface of an oil painting. I can't emphasize enough just how cautious you should be with bubble wrap, at the very least please ensure you face the bubbles out, away from the painting's surface - I have found that this works fairly well. The main thing to remember is that things will stick to a painting's surface even if it's an older painting and feels dry as a bone - oil paintings are tricky customers.
A sheet of cardboard or foamboard will be a good addition for protecting the surface of the piece from knocks. If you have accidentally dented your painting then please get in touch, dents can be fixed!
This is a personal preference, but I like to hang my paintings directly on top of screws (Rawl-plugged into the wall of course), I prefer not to use picture wire myself, although I do send all works out from my studio pre-strung with picture wire. I would say that picture wire is definitely safer (less likely to fall down), particularly if the piece is hung in a place where it may get knocked from time to time (shoulder height, corridor!), I speak from experience here. Also, hardly a revolutionary tip, but avoid hanging paintings from a single nail - again, speaking from experience, I am terrible for cutting corners sometimes...