When Rose premiered, my wife Laura and I were ready. We'd both seen a few classic episodes way back when before we met, and in 2001 I'd started seriously getting into Doctor Who, so we were watching classic episodes and listening to Big Finish audios, and I was reading books and magazines and online forums.
One surprise for us was Eccleston's performance. We'd seen him in several TV shows and movies. He was best known for doing intense dramatic stuff, and he did it very well. We hadn't seen him do anything like his portrayal of the Doctor. But he was still good, we loved the "lots of planets have a north," we liked the speed and energy of it. The bin and the fake Mickey we weren't so sold on, but we liked the fact that the show was setting out to be fun. There are many things I like about the 1996 TV movie, but it was short on fun and long on things that don't mean anything to new or casual viewers.
The first season wasn't perfect, but it was much, much better at working out what it wanted to be than TNG was in its early years. And much more likely to be rewatched in this house.
The one consequence of the new Who's success that still strikes me funny is that I can walk around Ottawa and see people I don't know wearing Doctor Who t-shirts and having conversations about it -- from teenagers to people of my own advanced years. It's common and ordinary to talk about Doctor Who with people at work or at the comic shop or at the pub, my inlaws, etc. Back in 2001 I was just happy that I had 26 years of TV Who and a lot of books and whatnot to dive into; I never would have expected a new series, much less that it would be so popular.