I'm torn; Tom Baker was the Doctor, but I enjoyed the flamboyant exuberance of Jon Pertwee.
As for companions, the luscious Leela has been mentioned, but I also loved Jo, the super-scrumptious Katy Manning in Jon Pertwee days, and liked Nyssa, Sarah Sutton, too. Some people thought Adric was a pain...
The villains; yes, some of them were terrifying to look at, but some of the more "normal" ones were maybe worse. Viz., Roger Delgado's elegant megalomaniac The Master, delighting in destruction; and I found the insane militarist the Graff Vynda-K chilling.
I've only watched a few of the "modern" episodes and haven't found them anything like as enthralling. Perhaps that's rosy-tinted nostalgia, but it just isn't the same show that I used to enjoy so much. Much more slick production, of course, but what use is that? It looks much like any other slick modern made-for-TV film. People used to snigger at the cheap production of classic Dr. Who, but maintaining any sort of willing suspense of disbelief of a big ask with a show of this kind. I thought the rough and ready, make do and mend look of the cheap production actually helped by making things more like real life. Now, things seem too bright and colourful; everybody is too well turned out in designer clothes, too clean and tidy; even the modern cybermen look like they're fresh from a cyber boy band. The classic "big ears" versions were more scary because they were humanoid but a travesty of humans.