I voted for epic.
All my initial games were played at normal. The games were fun, but unrealistic and a bit frustrating. The tech pace vs. unit movement on pangaea maps wasn't too bad, as war could be waged before the tech pace accelerated. Not so for continent and archipelago. If you wage a WWII Normandy-style assault in a normal game, it's possible to ship off macemen and catapults in galleons, and about the time they arrive, everything can upgrade to cannons and grenadiers. A few cities later, it's time for infantry and artillery. I have to wonder how it didn't get tweaked at some point during playtesting. I would never ask for (or want) total realism, but the current late-game tech pace is just insane.
Now I have played a few games at epic speed and like it more in every way. Research vs. unit movement is more balanced, and it doesn't seem to make games much longer. However, I am a slow player. If I play a "normal" game meticulously, it has taken anywhere from 10 to 24 hours depending on the victory condition pursued. I played one epic game in 8 hours (diplo), and another in 16 (domination), so it doesn't seem to make much difference--at least for me. That may partially be because I have gotten better at using my city adviser screen, and I don't spend as much time checking each city individually.
Unfortunately, I think the different game speeds affect the "fun" level depending on what type of victory you pursue. Epic speed makes military games more fun because you get to do more with the units you invested in. Peaceful victory conditions at Epic aren't as fun because the turns are more tedious. If you are a fast player, you just hit "end turn" a lot more often than in a normal gameno big deal. But for a micromanager you have to go look at a few cities on most of those extra turns, and that's a lot of added tedium. I fear this difference in the fun-factor is going to make players who usually play for peaceful victories heavily favor Normal, and warmongers favor Epic.
I like to play for a different victory condition every month, and I am hoping most games end up being Epics for the following reason: the extra time spent checking cities in a peaceful game is more bearable than only getting 10 turns to use a unit before it is obsolete in a military game. I fear I will tire of the latter very, very quickly.
I haven't played "Quick" yet, but I have a vision in my head of sending a swordsman off to a distant enemy city, and at the time he arrives, building an infantry in my capitol. I can't imagine ever wanting to play a "Quick" gameunless, perhaps, it's to test that theory.