Classic Who: Where to Begin
Third Doctor - Spearhead From Space
The plot - the Doctor has just been forcibly regenerated by the Time Lords so we first see him passing out as he tries to step out of the TARDIS. The Time Lords, in their infinite dickery, have basically put a steering lock on the TARDIS so he can’t go anywhere. The Brig doesn’t recognise him, the doctors trying to look after him are all convinced the others are playing pranks because his binary circulatory system and non-human blood, he’s without trusted companions Zoe and Jamie since the Time Lords took them away from him at the end of Two’s final serial, and the Nestene are trying to take over the world. Features include the radiant and quick as a whip lady of intellect Liz Shaw, the Brigadier’s moustache, plenty on nice outdoor shots (as opposed to the usual studio bound serials), and the infamous Three shower scene. It also works as a good introduction for UNIT, who feature heavily in Three’s serials, building nicely on the setup from The Invasion serial from Two’s era. Dandy!
Honourable Mention: Terror of the Autons (Introduction of Jo! Mike Yates! The Master!), Frontier in Space (it was my first Three serial and I caught on pretty quick. Jo’s pretty kickass and the space husbandness of Three and Delgado!Master is very apparent)
Not Recommended: Carnival of Monsters, The Curse of Peladon, The Monster of Peladon (in my opinion these are the weakest serials of Three’s era. naturally, this is a completely subjective opinion so if you want to start here by all means go ahead)