Just couldn’t avoid throwing in my two cents on this one. I have enjoyed both old and new Who and have been a “Whovian” since the 70’s. My all time favourite tele show is (no surprise) Battlestar Galactica; however its not really family friendly. BSG is for grownup time. DW is after dinner entertainment.
The New Who is a big (W)hoot. Lots of fun and fairly good special effects. Easy to jump into. The classics though are, admittedly, a bit more of a challenge to today’s audience. If you understand that the old Who was a product of its time, both in the approach to story telling and in the use (or misuse) of special effects, there are quite a few very enjoyable stories. Which are the best? It really depends on the audience. Kids seem to dislike anything in black and white and would prefer to avoid too much talky, talky. The stories are slower than what is expected in our frenetic times, but still quite good. There are a few groaners, however. Even with these caveats, they enjoyed and Unearthly Child – Hartnell’s first time in the TARDIS.
“My” doctor was Tom Baker and most of his stories are fun stuff. Robot shows his regeneration and initial silliness which the kids enjoyed but I couldn’t stand the horrid special effects in this one. I did enjoy the Arc of Infinity quite a bit as did the kids. City of Death was very good as well, but you might have to stop and explain things to younger kids. My young ones liked Pyramids of Mars, fairly simple horror. I enjoyed Talons of Weng Chiang (I loved Sherlock Homes) and Horror of Fang rock. Of course, one cannot miss the classic two Dalek stories from the Baker era. Not my favourites but generally considered quite good by others.
The other doctors have a few more clunkers but some wonderful stories. My son likes Pertwee whenever Unit is shooting the place up and nearly died of excitement when Unit starting shooting the place up in one of the recent New Whos. Both liked Davison to some extent and his last season is quite good. The kids also liked McCoy, though he has a few clunkers. (The kids liked Bonnie Langford – no accounting for taste)
As to getting some background on doctor who, you might want to check out babelcolour’s videos on Youtube. One is called a “fact file on the doctor” or something like that. It is cute and gives some background of the old series.