Flickerdart's selling on Russia is a good one, and Leecros' breakdown of the DLCs are good. My personal two cents on DLC is to get Way of Life, Sons of Abraham and Conclave right away, because they will be useful and add depth to anyone you're playing, no matter where. From there, you can pick and choose which different regions/faiths you want to try and pick up the appropriate DLC.
As to specific characters that are worth checking out, especially in 1066, it's hard not to go with the classic: William the Bastard. Can you help him get his historical title of William the Conqueror? The Saxons are not as much of a push-over as you may think, so having a decent understanding of the mechanics/relationships will help a lot.
I personally like the King of Poland in 1066. His stats are crazy, his realm has a lot of potential, but he is surrounded by threats: The HRE, Baltic Pagans, Hungary, Scandinavia, you will never be short of people to butt heads with.
The Jimenas of Iberia are good fun as well. Brother Kings at each other's throats with the Iberian Muslims waiting to pounce on the slightest weakness.
It's slightly later, but the 1081 start with Alexios Komnenos in Byzantium is a really fun start, though you'll probably want to get the Legacy of Rome DLC before you try that one.