Rather than dreaming up and planning out a new character, just assign numbers to all of the choices in chargen and then "roll" a completely random character.
I started with the http://linklost.com/occ/ and a http://www.mathgoodies.com/calculators/random_no_custom.html. The generator allows you to set any range for the numbers, so I just set the range to whatever was necessary (1-2 for gender, 1-10 for race, 1-13 for sign and so on) and moved down the list. When I got to favored attributes, I just generated 2 numbers from 1-8, and for majors, I generated 7 numbers from 1-21 (8, actually, since I got one duplicate).
And this is what I ended up with:
Race/Gender: Imperial / Male
Birthsign: The Serpent
Specialization: Magic
Attributes: Intelligence, Strength
Major Skills: Mercantile, Security, Sneak, Acrobatics, Light Armor, Hand to Hand, Armorer
Really not bad at all. It's odd, certainly, but I'm sure it's playable.
So then, carrying out the notion of randomness, I used http://www.silgrad.com/oblivion/rangen/ to come up with his name-- Arlowe Clanler.
Then, still pursuing randomness, I started his game with http://www.tesnexus.com/downloads/file.php?id=25591, an alternative start mod that lets you start the game in any of 45 locations, and includes a choice of "I don't know," which randomly starts you in any of those locations. And, luckily enough, he started in the house in Bruma, which means that he already owns it.
So that's it-- that's my newest character. Arlowe Clanler the Imperial..... something or another (I named him a "Wanderer," since I didn't know where he was going to start or what he was going to do). He puttered around Bruma for a while, doing this and that but not quite sure what his plans were, but as soon as he got out of jail from Arnora's quest and got the Mysterious Note, he dashed headlong to the IC. He definitely wants to join the TG. It's just a natural fit for his purely random skills.