Sixties Who didn't really have tight continuity - at most there was a cliffhanger leading into the next story but they were kept pretty vague.
You can jump from story to story, the missing episodes aren't a big deal - it just means you won't be able to watch every story, though all the missing stories are available on audio.
Without the missing stories, you have the confusion of Companions changing in those missing stories, which can be distracting, though
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?