The only book that I read new was the fifth one. I started reading the first, then the second, then the third...
Once I was done with the fifth one, I thought: "Oh no! There isn't a next one yet!"
I hope that I can remember what was going on in the fifth book by the time I get to read the new one.
I'm counting on a pretty thorough recap in the introduction chapter.
I have an idea how it is going to end... Want to hear it?
I think that Harry (near the end of the last book) gets killed by Voldemort; however because of his relationship with a phoenix (the feather in his wand) Harry will come back to life and eventually win the final showdown.