Baker was always my favorite Doctor. He made a very touching appearance in a recent special.

When the show rebooted after its interregnum, the writers created a backstory of how the Doctor, after participating in a brutal war between the Time Lords and the Daleks, decides the only way to end the war is to destroy them both. This has haunted all of the new incarnations, with various effects. Sure, he is still inscrutable as hell, but now he is much older, darker, and careworn. By this point, he has lost so many companions that this haunts him too. Despite this, he is can still be silly, even childish, but prone to an anger that can destroy worlds.

Also, the Master is now Missy.

If you have 77 minutes to spare, watch the 50th anniversary special, The Night of the Doctor. Excellent episode, even if you haven't been caught up for decades.

Another very good episode is Vincent and the Doctor. I coerced Mrs P., who has never seen a single episode of Doctor Who, to watch this episode, knowing well her fondness for Van Gogh. The final scene had her in tears. If were you to watch only one episode of the New Who, make it this one.

PS EDIT:

Yes, he's been married, but she moves in time backwards to him. His first kiss is her last. "Spoilers...."