Quick thoughts: I really enjoyed the episode. If I were ranking it with my rating system for the audios, I would probably put it on the high end of the Good scale. I generally think that most of the "introduce a new Doctor" stories are weak stories. My least favorite of the classic series would probably be "Time of the Rani" while my favorite would be "Spearhead from Space". As for the new series, my favorite (and this would be my favorite Doctor introduction story overall) would be "The Eleventh Hour" which I rate about as highly as all of the best Who's from the modern era. While I didn't like "Deep Breath" nearly as much, it's still miles better than "The Christmas Invasion" which I find fairly torturous to sit through on repeated viewings until the Doctor finally wakes up.
I enjoyed this episode a lot more. The story was solid, if not spectacular. But, I just love what I have seen so far of Capaldi's Doctor. I think many long time fans of the classic series are a bit predisposed to like the 12th Doctor. He just feels more like a classic Doctor than any of the modern versions have. I also think Jenna Coleman was tremendous. A lot of my friends don't really like Clara very much, but I have always found her to be fun. One thing's for sure, Jenna is an excellent actress. I thought she was riveting in the breath holding scene. Of course, the ending minutes were emotional and lovely. I am very excited about this new season of Doctor Who, and I may end up writing more of these first impressions for each episode.
I hope to have a review of "Project: Lazarus" up in a day or two. I need a night where I am not exhausted to write it.