I hated the early Whos with passion. I had friends who were enthusiasts and knew everything about the show, but whenever I tried my brain tried to crawl out my earholes.
For some reason, my wife and I decided to try the reboot (I refuse to write N-Wh-.) We’ve gotten six seasons in.
Season 1 with Eccleston was pretty good because he was great with rage. David Tennant is a fine actor and managed to make the role his own. Matt Smith is a bit of an acquired taste but his quirkiness works for an alien, when the writers don’t forget he knows everything about earth.
I would start with season 1. Although the show is littered with references to the earlier seasons, everything you need to know is easily graspable. The showrunner for seasons 1-4 was Russell T Davies. He had a mania for grouping a dozen extras in face-covering costumes and having them march against the good guys. Every episode involved saving all of Earth from destruction. London is destroyed multiple times and people somehow forget about it. The Daleks and Cybermen are beloved by the oldsters, but they are the worst enemies. I’d say skip any episodes with them except for the giant super blockbuster time and space is periled season endings that Davies kept dropping on our heads. He gave us fun while yelling in our faces.
The best episodes were the small quiet ones without armies of attacking aliens. “Blink” was written by Steven Moffat, who became showrunner with season 5. I was hoping for great things. We didn’t get them. However, the show went smaller. Moffat doesn’t do armies of marching aliens. He doesn’t destroy large parts of Earth. He wants to emotionally involve the viewer. The problem becomes that emotions triumph over sense. If you thought that Davies power-jumped over enormous plot holes, Moffat builds gorgeous spiderwebs and just lofts from the outside to the center. Sometimes it works, sometimes not.
You also need to judge seasons by how much you like the companions. The Doctor is famous for his companions, usually - definitely not always - impressively beautiful young girls. Are they hired for looks over ability? Usually yes. Are they used impressively? They are given to exclaiming that they don’t know what’s going on, just like the viewer, and tend to be given answers that leave them more confused than before, just like the viewer. Moffat tried to make his companions more involved, but nobody can or should care about their feelings. If the show isn’t completely about the Doctor it isn’t worth watching.
Just one person’s opinion. I’ve tried not to get into spoilers about seasons we haven’t watched, but the general consensus is that everything after Smith is a disappointment compared to these early seasons. As with superhero comics, every good plot and every plausible character development is explored but the next issue has to be written. Maybe starting with the 13th doctor and working backward 12, 11, 10, 9 so the show gets better and better is the way to go.