I’ve always loved this show since I saw it on my local PBS station in the late '70s (yes, I’m that old). It was the 4th Doctor, Tom Baker, whose episodes they had on at the time. So naturally since he was the first I was exposed to, he became my favorite. Although the 3rd, Jon Pertwee, is a very close second. 
Both Ocelli and I have been collecting the 3rd and 4th Doctor DVD as they’ve been released. But BBC home video doesn’t seem to be releasing them in any kind of pattern I can decipher. Most recently they released the 3rd Doctor eps Terror of the Autons (which features both the first appearances of Jo Grant and The Master) and the final 3rd Doctor ep Planet of the Spiders. That last one will be especially bittersweet now, as I understand that was the last ep that Liz Sladen (Sarah Jane Smith) recorded a commentary track for before her passing a couple months back. 
So far, I think there’s only a few episodes left of either Doctor that we don’t have. For Pertwee, the only episodes they have left to release now are The Ambassadors of Death (which they’re hard at work doing a color restoration of), The Mind of Evil (also a color restoration job), The Daemons, The Colony in Space, Invasion of the Dinosaurs and Death to the Daleks.
For Baker, there’s only a few left now: Terror of the Zygons, The Android Invasion, The Face of Evil, The Sun Makers and The Nightmare of Eden.
And who are my favorite companions? That’s easy: Sarah Jane Smith, Jo Grant, and Brigadier Lethbridge-Stewart and the rest of the UNIT family! Although more recently I became quite fond of Rose Tyler and Amy Pond.
And enemies? Well, although I have a soft spot for the Cybermen, Sontarans, Silurians and Sea Devils, nothing but nothing tops the Daleks!