I'll likely pick a story from each Doctor:
1 - The Dalek Invasion of Earth
The first Hartnell I saw, back in November 1988 on the 25th anniversary. Might watch An Unearthly Child ep 1 as well.
2 - Orphan eps
Not too fond of his surviving complete stories, though Tomb and Seeds come close. May just chose a selection of orphans.
3 - Inferno
No contest here...
4 - Genesis of the Daleks
Haven't seen it in years so should be a good catch up.
5 - Earthshock or The Five Doctors
Two favourites as a kid.
6 - Attack of the Cybermen
Revelation is my favourite but I haven't seem this in years.
7 - Silver Nemesis
Same reasoning as 6.
8 - The Movie
9 - Parting of the Ways
Best of his year IMO
10 - Doomsday
My favourite Tennent ep. Either that or Gridlock. Or the Season Three Dalek eps.
11 - The Eleventh Hour
The only episode of his I truly enjoyed.