I could recommend you watch the whole damn lot, which you should do really. However, I will give you my limited list of three recommendations per Doctor that I think you might enjoy:
First Doctor: The Daleks Invasion of Earth, The Time Meddler, and The Rescue.
Second Doctor: Tomb of the Cybermen, The Enemy of the World, and Power of the Daleks.
Third Doctor: Day of the Daleks*, The Daemons, and The Sea Devils.
Fourth Doctor: Talons of Weng Chiang, Genesis of the Daleks, and The City of Death.
Fifth Doctor: The Caves of Androzani, Kinda, and Earthshock.
Sixth Doctor: Revelation of the Daleks, The Two Doctors, and Vengeance on Varos.
Seventh Doctor: The Curse of Fenric, Ghost Light, and Survival**.
Ninth Doctor: The Empty Child/The Doctor Dances, Dalek, and Rose.
Tenth Doctor: Human Nature/The Family of Blood, Blink, and Midnight.
Eleventh Doctor: Vincent and the Doctor, The Eleventh Hour, and Night Terrors.
Twelfth Doctor: Mummy on the Orient Express, Thin Ice, and Twice Upon Time.
Thirteenth Doctor: Rosa***, The Haunting of Villa Diodati, and Village of the Angels.
* Day of the Daleks is what inspired the X-Men comic book story Days of Future Past.
** Survival has a very similar feel to the revived series stories. Rona Munroe who wrote it is the only Classic series writer to return to write for the revived series.
*** This Bafta winning episode features Rosa Parks and is in my opinion the best story of the revived era.