I have been 100% positive about Day of the Dr and An Adventure in Space and Time 
Peter, on picking up somewhere in Dr Who: I think any of the advice mentioned earlier by third parties, or by Emerald, is fine. I’ll just give you some perspective on the old episodes.
In Australia, Dr Who was a childhood staple for my generation, as it was on Mon-Fri on our national broadcaster (the ABC) somewhere between 5 and 6 for over a decade. But they never showed the black and white ones in that timeslot (I think once they ran some Troughton episodes). So we endlessly gestated on a huge loop of Jon Pertwee, Tom Baker (my fave), Peter Davison, and to a lesser extent, Colin Baker and Sylvester McCoy.
In 2005, after not having screened Who for years, the ABC started to run the entire show in chronological order at 6pm Monday to Friday, from the beginning, starting with Hartnell’s first episode, ending with McCoy’s last. What was skipped were the missing/damaged episodes and (ironically) most Dalek stories, because there was copyright combat with Terry Nation’s estate at the time, their attributed creator.
In spite of being in this fan club, this was the first time I’d seen 95% of the black and white ones, and it was great to do it in order and in the old style of one a day. I discovered that I loved both the first and 2nd Doctors, never having known them before. The only Dr who went down in my estimation during the re-runs was Jon Pertwee, whose snootiness suddenly wore on me as an adult.
Anyway, all I’m saying is - if you’re worried about missing episodes and such, the majority of Dr Who fans now haven’t seen them, and some of us didn’t see any black and white stuff at all for most of our lives.
I don’t doubt a show with this much material looks daunting to anyone. But I guess that’s why Dr Who fans are lucky. There’s acres of it.
My own advice is to at least dabble in anything from Peter Davison or earlier first. See what old Who was like, as aesthetically I don’t think it was like anything other than itself. I feel new Who is aesthetically like most adventure television of today.
-Wade