So somewhere between classic Who and new Who the Time War just happened?
Yep. It was RTD's narrative device that allowed room to maneuver between the two era's. It allowed him to change details he needed, with a simple, blanket answer. Also, it allowed him to imbue the title character with a personality device or motivation that he could use to cover general television character conventions. Beforehand, The Doctor....as an emotional person....is a blank slate. Only rarely was the audience allowed access to his personal pain or joy. Want a stiff upper lip Doctor? Watch the 5th Doctor barely blink an eye when his companion Adric gets killed. Modern stories would take a season to deal with the personal trauma he might suffer. Back then, it was glossed over in about five lines of dialogue. I mean, sure, Adric was a complete twat. But, still, if Tennant's going to get misty over a clone he's known for an hour, then he would have lost his mind over Adric. But, I digress...
Anyway, while I support your intention to delve into Classic Who, I would add a few words of experience. A lot of what modern Doctor Who has built up in your mind as this impossible mythology of adventures and grandiose tales will absolutely not live up to your imagination.
For one, as you probably know, the budget back then was about as much as they pay the people that cater their lunches these days. So, it's pretty much a "stage play" environment. If you can't see past the surface-level of tv shows, then you won't enjoy old Who. It requires something that a lot of modern audience seems to lack: imagination. Now, it's not the modern generation's fault, though. The standards set by movies and television today is staggering. But, if you can't do without special effects, don't bother with Classic Who.
Second, a huuuge amount of what fans love about old Doctor Who is that it's a tie to their childhood. Nostalgia of the moments we lived through paint a picture of Doctor Who that cannot be matched by actual fact or show. So, when someone tells you how wonderful an episode is, you take that with a grain of salt. On the flipside, my wife (for example) has found some Classic Who to be just as good as I've told her. Sometimes better. So, in the end, it's all up to the individual.
That said, I too recommend
Genesis of the Daleks, as well as the
The Keeper of Traken/Logopolis/Castrovalva three-piece boxset.
City of Death is a damn good Doctor Who (written by Douglas Adams). So is
Caves of Androzani. But, those last two don't have The Master, Cybermen, or The Daleks in them. Try the 5th Doctor's
Earthshock. And, as previously mentioned, the first Cyberman story
The Tenth Planet is complete save for the final episode (of which pieces still exist, as well as audio recordings that will fill-in the rest of the story).
Sorry this thing is so long.
