More familiar with modern Doctor Who than the classic show or other media, but have seen a decently-sized cross-section of the classic show since roughly 2011. Favourite writers are probably a tie between Russell T Davies and Steven Moffat, with Jamie Mathieson and Matt Jones probably not being too far behind. Anything more specific for a "favourite episode" is impossible. For Moffat, this still holds true as of 2016.
Also, even if they're not quite classics, I quite liked Daleks in Manhattan, Evolution of the Daleks, the Slitheen family episodes, Love & Monsters and Torchwood: Miracle Day, or at the very least, find more good than bad in them.