Just jump in: the original series is serials (4/6/occasionally 10 episodes) but there's rarely interconnection between stories (and ifi it is, it's stuff you'll appreciate later, as the events of the last story have an effect on the main characters).
But basically, just jump in and watch. Avoid the first two Doctors unless you're OK with stuff being in black and white. The fourth Doctor is a good starting spot as few serials are more than four episodes long (ie, 100 mins)... oh, and Tom is a great Doctor.
But if you like the Doctor as an odd hero, you'll probably like every version of him. (And then argue about why you prefer some of him to others).