I know that, for me, I always loved the concept of Doctor Who. Watched a couple of third, fourth and fifth Doctor stories when I was a kid because my uncle had them on VHS. Wasn't in love with the show, but I was familiar with the concept. Watched the Douglas Adams episodes when I got into Hitchhikers Guide when I was 13 or so. Again, kinda liked the concept, but at the time the show was just too old for me to appreciate.
Fast forward a couple of years when the show was rebooted with Christopher Eccleston. Wanted to give it an honest shot, because I always had this weird fascination with the show. I actually really liked the first series back in the day, because it felt unlike anything else on tv at the moment, but there were a lot of episodes I didn't really like (Big Brother spoof, anything with the Slitheen, etc.). Which was fine, it was just a first series. Then David Tennant came around. I liked him, but not more than that. Really, really wanted to love the show. When it was good, it could be really good. When it was bad, it was embarrassingly bad. The show had so much potential, but never really fullfilled that completely for me. The cheesy melodrama certainly isn't for me, and there's just so much of it in those seasons. Gave up on the show numerous times, tried again and again. The was the occasional episode that I really liked, but it was almost always followed by a couple of stinkers.
Then I heard that the show was getting a new showrunner. I remembered Moffat's name, because he wrote a lot of the really good episodes. Gave it another honest shot. His season, season 5, was nothing short of amazing. Exactly what I wanted the show to be. Funnier, better written, more engaging plots, better acted. Loved the show so much that I started rewatching all(!) the classic series episodes. Season 6, while a bit less cohesive than season 5, is still pretty great in my eyes. Season 7 didn't really work for me, felt more like it became a bit of an imitation of itself. Some good moments though. But for me, season 5 and season 6 still is something very special.
Whenever I try to get a friend into Doctor Who and they want to start with either Eccleston or Tennant because they heard so much about him they give up very quickly, and just can't understand why I would want to waste my time with a show like that. I'm a bit more fond of those episodes these days because I can forgive their faults more easily, but I just don't think they hold up to other modern tv series. Nowadays I just start by showing people Sherlock, which is a bit more approachable to most people, and offer them season 5 afterwards. I don't even start with Blink, as I don't think anything in that story is really needed to understand the later stories. The Silence in the Library two-parter is the only one that's really important from a plot perspective. Not the easiest episode to start with though, so I just show that after season 5, to give a bit of backstory to River Song. The Eleventh Hour is just the perfect introduction episode, in my eyes. The world opens up very nicely during those first couple of episodes of season 5, and does it a lot more gracefully than season 1 did.
Tastes differ and all that. I honestly really like every actor who ever played the Doctor. I just don't like every era, in terms of production values, style and plot.