Catch The Dead Planet from Hartnell's work; don't bother with the rest. There are damned few episodes of Troughton's work that survived the BBC purges intact, and it's downright painful to watch the kinescopes of those that did. (This is too bad; Troughton's a good actor.)
Start with Jon Pertwee--the first decent doctor. Watch him and Tom Baker. Don't bother with Peter Davison. Colin Baker's only worth watching to catch up with DW continuity in the Trial of a Time Lord thread. I personally love Sylvester McCoy's work, but that's me.
Skip Eccleston altogether--a potentially interesting character development that never got close to being realized. Go right to Tennant; you could watch his stuff twice over if you're so moved. I cannot abide Matt Smith, but again--that's me.
I'm still lobbying for a female Doctor for the next incarnation.