How much of classic Doctor Who is serialized? Can I just jump in anywhere?
Every Story is Serialized, though each story is fairly independent (From Tom Baker forward, most are 4 episodes of 25 minutes each, a few 6 episode stories). Prior to Tom Baker, most stories are 6 or more episodes, with some that are shorter.
Most stories are are independent. The Key to Time Series is 6 individual stories, but, all have a Quest running through them (Ribos Operation, Pirate Planet, Stones of Blood, Androids of Tara, The Power of Kroll, The Armegeddon Factor) . The E-Space Trilogy, is basically only connected in the fact they are in a different universe (Full Circle, State of Decay, Warrior's Gate) and then the end of Tom Baker's Run/beginning of Peter Davison's all involve The Master, and kind of lead into other (Keeper of Trakken, Logopolis, Castrovalva). For the most part, though, yea, you can pretty much jump in anywhere and watch in whatever order (Though I like to go through all the stories in order by Doctor, as the Companions provide a bit of a story continuity)