My picks for Best Doctor Debuts in Doctor Who history, I'm counting their debut episode, not the first time they appear
http://www.ranker.com/list/the-best-doctor-debuts-in-doctor-who/ryanwitalison,
Castrovalva
The 5th Doctor's debut
Spearhead from Space
The Debut of the 3rd Doctor as well as the return of Brigadier Alistair Lethbridge-Stewart and UNIT
The Christmas Invasion
The Tenth Doctor's debut
The Power of the Daleks
The Debut of the 2nd Doctor, sadly none of the episodes survive on film. Exists today only in Audio format and in reconstructions
Robot
The 4th Doctor's debut
An Unearthly Child
The Very First episode of Doctor Who
Enemy Within
The 8th Doctor's debut and only real TV apperance
The Eleventh Hour
The Eleventh Doctor's debut
Deep Breath
The Twelfth Doctor's debut
Rose
The Ninth Doctor's debut, and return of the series