Scions of Patria (from the major modmods).
Because it's like... like... like someone designed a civ with all of my preferences in mind.
And because they're so different from the other civs. My liking of a FFH civ pretty much tracks with how different it is from standard play. I tend to alternate between Revolutions DCM - for when I want to maximize a game's challenge - and FFH, when I want something novel. The Illians, with their Ritual-based victory condition, is currently my other favorite. I worked my way through many of the civs, exploring it over many games and then moving on to another. I still occasionally play a completely Lore-centric game as just about any civ, depending on what I'm in the mood for.
A nice thing about FFH is that there's generally a civ (or civ/religion combo) for whatever whim you feel like indulging. I'd say look over the basic 'pedia entries and just go for whatever looks fun at the moment.
Not counting the Scions I've probably played the Svalts (I'm often in the mood for evil sneakiness), Calabim (vamp mechanics and fun lore) and the Khzad (low magic) the most.