I’ll be the contrarian here and suggest that—especially if you’re OK with trying one book out of order and then going back to read the rest just so that you can get a feel for the books—that you start with Dead Beat. It was written as an introduction for new fans when the Dresden files TV show was getting ready to come out. It really shows off some of Jim Butcher’s strengths as an author after he got his feet underneath him. It’s the book that the fairly well-known (spoilery) meme is from.

As to Dresden’s, chauvinism, this older Reddit comment, probably addresses it as well as any I’ve seen. I will say that it isn’t just treated as though it must be there. There are strong, textual and sub-textual reasons why he acts and thinks the way he does, it’s never treated virtuously, it does get him in trouble, and he does realize he has to be better.