To elaborate a bit, a large percentage of Who fans consider “Blink” to be the greatest episode ever. When I first saw it, it blew me away, and I had already been a fan for close to 20 years. I’ve watched it at least 6 or 7 times and I still enjoy it. By contrast, some of the more recent episodes are too “drama-heavy” for my taste – the whole Rose period, and the River Song stuff, all kinda detracted from the quirky-time-traveler episodic flavor that attracted me in the first place. In short, there are a wide variety of styles over the years, and you are likely to find some you like, and others you don’t.
For modern Dr. Who, I tend to prefer Capaldi - some of the episodes in the most recent series were fantastic. I also very much liked his predecessor Matt Smith, especially his first episode (“The Eleventh Hour”), but some of his later ones became too drama-heavy for my taste.
As for the older, “classic” Who, Tom Baker is certainly the quintessential Doctor. Way too many wonderful episodes to list. “Genesis of the Daleks” is one of the best, with a fantastic climax… some people consider it the best episode ever. It also would give you a sense of the slower-paced approach of the day, where a single story stretched and developed over a few weeks. Some younger viewers find that pace too slow, but in my opinion there’s no better way to spend a relaxed, rainy saturday morning with some coffee and toast 😃
For these older eras, I have known some women to prefer Peter Davidson, because he was good looking. A former fiance of mine had a big crush on him (she is the one who actually got me hooked on the show). Davidson was in several excellent episodes… “Caves of Androzani” for example. I liked Sylvester McCoy too, and although he was in some dreadful episodes, he was also in a few excellent ones (“Curse of Fenric” and “Remembrance of the Daleks”). Newcomers should avoid Colin Baker episodes (not to be confused with Tom Baker, mentioned above).
One of the cool things about the series, is that each Doctor is encouraged to inject their own “style”. So the various doctors are VERY different from each other, while still retaining some irreverent British humor as a consistent thread. The Dr. Who universe also is replete with a number of repeat-villains. The Daleks, The Master, The Cybermen, etc. It is interesting to see how the villains changed as the budget increased over the years.