
Dragon Age: Origins contains 6 different origins, each unique in their own way, and each will affect the way you experience the game. Neither origins or classes are gender restricted. All of the origins have set surnames (á la Mass Effect). You can see the possible race/class/origin combinations here.
Personally I'll go for the Mage origin (human male) on my first run (doh, I bet no one saw that coming

Human Noble l City Elf l Dalish Elf l Mage l Dwarf Commoner l Dwarf Noble
I'll end this post with a quote from the game:
Morrigan: "Tis cold in my tent, all alone..."
Human Noble: "Then get a thicker blanket."