When you say Netflix, which version do you mean? If you have streaming-only, there is a very limited supply of classic titles available, less than 20 of the 130+ released stories are available via streaming.
Of those, The Aztecs is a good introduction to the First Doctor. The Three Doctors is a reunion story, with the first three Doctors working together to solve a problem. It will give you a sampling of their personalities.
The Fourth Doctor is the most-represented on streaming. Try City of Death. It's a classic, and a fun romp. His entire "Key to Time" season is also available, and it introduces fan-favorite companion Romana.
The Fifth Doctor's final story Caves of Androzani is frequently voted the most favorite story by classic Who fans. It also (briefly) introduces the Sixth Doctor. That is actually the only Sixth appearance via streaming.
I don't remember which story the Seventh Doctor has on streaming, just that it's not one of the better ones.
There will be other answers should you have the dvd option.