I voted for Medieval, for a few reasons:
The earlier ages used to be my favorites in Civ2 and 3, but a lot of the joy of expansion has been taken away from the starting game. (Which is a good thing, don't get me wrong; thinking you might be in serious trouble because you didn't beat a neighbor to a fourth city was joyless in a different way.) The thrill of exploration never goes away for me, but all the other headaches have dropped this era from "most favorite" status.
The Medieval era has the best range of choices, options, and unit viability, at least on Noble. Choices include picking between new buildings and new units, and how they fit into the situation as you see it; which direction to expand the more optional cities you're going to build (the first three tend to be fairly clear-cut, eh?); and picking a direction to research based on something other than the terrain is nice.
Options: you have enough of an empire at this point to start feeling as if you're headed somewhere, and have something to work with. You also have the feeling, or at least I do, that you can make a mistake and still recover from it, in a way you can't when you have two cities and a third on the way.
Units: this is an era when the old units aren't so obsolete that sending them off to war doesn't feel like a way of managing your treasury. Horse Archers and Chariots can at least nibble on Macemen (and Longbowmen who actually venture into the field), and Archers with the right promotions are still almost good enough. The mix of new and old units means you have to think a bit before you use them, too, unlike the arms race that starts with Gunpowder and continues to the end of the game.