I wish I still had all my old character sheets, but I think they're all long lost -- probably thrown out at some point.
I've been RPing since 1986, and for most of that time, I've been the GM/DM. While I don't recall anything about the first character I played during that very first session of D&D, I do remember that when I got a chance to actually play, I favoured the thief class, with the cleric class coming in second.
The earliest character I can remember was what I would consider the first character that ever had a true personality (read: he wasn't just me). Father Edward was a 1st level cleric originally (I think he gained a couple of levels during that campaign) in a D&D Red Box game that my younger brother ran. This likely would have been in the late '80s -- or maybe 1990.
My goal with Father Edward was to be a pious, monk-like man who had spent his entire life in a monastery (these weren't the AD&D monks; I pictured him in a habit and mostly being unexceptional when it came to violence). I had a couple of quotes I regularly used for Father Edward (I think I called the others "my son" a lot). He often talked down to the other adventurers in the party, but he was a loyal friend who spent most of his time pulling clean-up duty after battles.
Another early character I remember was a thief, originally in D&D Basic and then later created again for AD&D 2nd ed. (I never played AD&D 1st ed.). Einar Lightfingers was named after a thief character in a fantasy novel called The Sleeping Dragon, which I discovered in 1990 when I entered high school.
Lightfingers, as he was mostly referred to, was the type of thief you didn't want in your party. Like the character he was named after, he had a habit of stealing from whoever he could -- even his own adventuring buddies. He was a greedy, little worm of a man.
Ah, good times.

Chris