I don't know about oiling them. I don't recall ever doing that and I've had mine for over 30 years. I usually just wipe them down with a damp cloth when I'm done. I figure there's enough "fat" that gets into them through use.
As for storage, I have two like the ones you purchased and the way I store mine is that I've put a cup hook in one end of each and simply hang them on an "eye" hook from under my upper cabinets. Does that make sense? It's late right now but, tomorrow, I'll take a photo and show you.
"As a girl I had zero interest in the stove." - Julia Child
This is real inspiration. Look what Julia became!