I have been referred to as an expert on the classic who. Been watching since I was about 9. 37 now. I will pick a story per doctor that might give you a wide variety of shows to watch.
Although off the top of my head, I would recommend TERROR OF THE ZYGONS as the first one. Unfortunately, it isnt on the list of DVD's yet. How Horror of Fang Rock makes it before a Douglas Camfield classic I will never understand.
1st and 2nd Doctor. Pick up the LOST IN TIME double set. great value for money and it has a nice mix of episodes, historical and sci fi.
The following is a top two list for each doctor except doctor 4. He had some good stuff. These are a DVD
1st doctor :doc1: THE AZTECS
a great historical.AN UNEARTHLY CHILD
just the first episode, the rest is crap
2nd doctor :doc2: TOMB OF THE CYBERMEN
Cybermen!!! THE MIND ROBBER
the weirdness factor recommends it
3rd doctor :doc3: INFERNO
very unusual premise for who even if it is a long story it keeps up the paceCLAWS OF AXOS
The Master and it is only 4 parts :master:
4th doctor :doc4: ARK IN SPACE
Great first night for the new doctor, he has a great speech about Homo-SapiensGENESIS OF THE DALEKS
I am not a fan of the Daleks, but Davros in this one makes it SO compelling to watchPYRAMIDS OF MARS
Gabriel Woolf as Sutekh almost outshines Tom Baker He was also the voice of the beast in Impossible Planet and Satan PitCITY OF DEATH
great fun and lalla Ward is so cute in her schoolgirl outfit;)
5th doctor :doc5: EARTHSHOCK
Many classic moments and the commentary track is greatCAVES OF ANDROZANI
great serious sendoff from the pen of Bob Holmes
6th doctor :doc6: MARK OF THE RANI
I enjoy all the location work and Colin is doing a great job in this one as he shows he DOES care for PeriTWO DOCTORS
It has both Pat Troughton and the Sontarans, TALL sontarans
7th doctor :doc7: REMEMBRANCE OF THE DALEKS
guest cast and a nice story without getting too bogged down in the shows historyCURSE OF FENRIC
Creepy period piece and great for those who like a good old fashioned monster story
A good VHS is MORE THAN 30 YEARS IN THE TARDIS
a great fun retrospective. Made before the movie came out.
I also enjoy the refernce books for the show too.
I will say I am SURE that my list will not meet the criteria of others lists, but hey this is MY list.