I'm backlogging, so this may be handled already, but I'd say just start reading the novels in order; they aren't that long. If you must pick three, I'd probably go 1 for Dresden himself, 3 for Michael, and 5 for Nick. As I recall, the fey are all spread out in there well enough to make up for it. On the very minus side, I don't think that gets you into some of the other, very fascinating, characters.
Another option you have is Side Jobs and Brief Cases, the short story collections. They occur between the novels. Major spoilers, of course.