I have already watched all previous seasons of Doctor Who (2005) and am waiting for the next season. I want to watch Doctor Who (60s) series, but it's not easy for me to watch 700 episodes in Black-and-white. I'd happily skip an episode if it's not important.
By important I mean, it must have a connection with currently running series (which can serve backstory or something). Or, it must be historically significant (popular or something).
What are the important episodes from the original series which can extend my knowledge of current series?