Mine was Destiny of the Daleks after which i watched it regularly, first appearance by Lalla Ward, so was the first female companion for me.
I personally really like her and she is one of my favourites, being a time lord/lady too gives her character an interesting dynamic i feel, and i think she's really cute too.
My first run in with other original Doctors was during the Five faces of Doctor Who repeats in 1981.
An Unearthly Child
(Monday 2 to Thursday 5 November 1981)
The Krotons
(Monday 9 to Thursday 12 November 1981)
Carnival of Monsters
(Monday 16 to Thursday 19 November 1981)
The Three Doctors
(Monday 23 to Thursday 26 November 1981)
Logopolis
(Monday 30 November to Thursday 1 December 1981)
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MIKE: I've got it! Peter Cushing! We've got to drive a stake through his heart!
VYVYAN: Great! I'll get the car!
NEIL: I'll get a cushion.