I don't know that I actually qualify as a fan of the series. I really like some of them, but I've not been a big fan of most so take my input for what it's worth knowing that.
I'd start with 4 skip 5 but play 6, 7, and 8 then skip 9-14 and play 15.
As far as picking a favorite, or listing 4,6,7,8, and 15 in any kind of favorite ranking, I liked them all about equally and a whole lot. Some of the best games ever made.