Yeah, read the Dresden books in order, although it takes two or three books for the series to really take off. There is an overlying story arc and people that appear constantly and aren't properly introduced each time they appear. That said a character named Michael isn't properly introduced at all.
Yeah, it's like you just open book 3 I think and there he is as if you know him already.
That being said, definitely read Dresden in order. The first few books aren't great, so if it's absolutely not your thing you can start either from book 3 (Grave Peril) or book 7 (Dead Beat), although I wouldn't recommend skipping anything from Grave Peril onwards. There are plot points that are absolutely essential to the overarching narrative there. That being said, Dead Beat was designed by Jim Butcher to be an alternative entry point to the series, so if you absolutely can't stand the writing in the first six books, you can try this one.
In my experience, I had trouble with the first two books, the third was 50/50 for me, but I was hooked with the
Summer Knight, the fourth book in the series, and it just kept getting better and better from there. I'm in the middle of my re-read (on
Proven Guilty right now) and I can't wait for the next two books to come out.