I'll preface this by saying that I haven't yet watched the New Year's episode of Doctor Who, but I have watched all the other new episodes.
The idea of this character being female for the first time sparked, well, lots of conversation. Strong opinions. While I didn't exactly feel the necessity for introducing a female Doctor, I didn't want to feel too deeply about it either way and in any case, I thought it would be better to just wait and see how it all went. After all, I wasn't the biggest fan of the twelfth Doctor, so I was probably already okay with the idea of liking some of them and others not so much.
When I started watching the show, though, it was like we just had another Doctor. They don't try to make much of the fact that she's female and that's the point: it's still the same character. And Jodie Whittaker also just approaches playing the character; she doesn't try to infuse the character with femininity on purpose or anything. She just is and that was the best way to go about it. So anything female about her is just a natural part of it all.
There are, of course, the moments when it does come in to the plot. If they're in historical places, then of course it makes a difference for the Doctor to be a woman than a man; the believability would go down otherwise (I mean, we all know this is fiction, but you know what I mean). Still, even when it needed to be an aspect of the plot, I appreciated that the plot never revolved around this.
Thirteen's companions are more reminiscent of the First Doctor's posse. Not just one companion to flirt with aka. Rose and Ten (though I did love them) or Amy Pond and Eleven. A group. The Doctor is great when he has a whole group, not just one companion. That also gives more space for the plot of each episode; you have more material to work with.
There was something fresh about the whole feeling of this season. Getting a new writer in obviously reworks the whole tone. It was great to have episodes that were just adventures, like before. Everything can't be a facing-the-end-of-the-universe thing because that gets old, as does having the same character die multiple times. It's fun at first and then it's draining and then it has so much weight that it has no weight. So it's better with such a long-lived show as this to go back to that lighter weight. To have the peril within the episode and that's it. To have the fun skittering over to the past or a new planet or whatever.
They also had a good mix of settings. Historical, present, future, Earth, not Earth, space, land, aliens, no aliens (or kind of no aliens). That's the fun and imaginative element of the show.
So I was pleasantly surprised by this new season. I liked the Doctor again, was entertained once more by that character. And I enjoyed just going along for the adventure of each episode, just a fun hour of exploration.