Even-more-dysfunctional-than-usual private eye

Ken Bruen's Jack Taylor series. If you like your protagonists self-destructive, occasionally sober, alcoholic, and drug addicted, miserable in relationships and smart enough to be aware of all this, have I got a series for you! Could it be more light-hearted? One of the attractions is that the books take place in Galway, Ireland and you get plenty of local flavor. Man, you can almost taste the Guinness and chips. The mysteries are pretty good, the side characters interesting, and the books are fast reads. As usual, I started with the most recent book in the series. That worked out OK, but I wish I would have read them in order. Here's a list so you can avoid my fate.
Book 1 The guards
Book 2 The killing of the tinkers
Book 3 The Magdalen martyrs
Book 4 The dramatist
Book 5 Priest
Book 6 Cross