In keeping with the theme, I think we should avoid the Spiritual trait (half price temples? - we don't neeed no stinkeeng temples). Therefore, I would rather not go random. This also means none of: Asoka or Ghandi (Indian); Hatshepsut (Egyptian); Isabella (Spanish); Mansa Musa (Malinese); Montezuma (Aztec); or Saladin (Arab).
Actually - maybe we should preselect those as our opponents.
Given the no-religion/happiness issues, I do not think health will be a limiting factor so Expansive is the trait I think we least need. So I would put Victoria (English); Bismarck (German); Genghis Khan (Mongolian); Cyrus (Persian); Julius Caeser (Roman); Peter (Russian);
As I said in my earlier post: I think our biggest handicap is going to happiness and culture - Creative combats both of these by giving quick expansion and cheap theaters.
Then again, the other problem is going to be Diplomatic: with closed borders and no common religion, we can count on having no friends. Ever. We should plan on being at war pretty much constantly once we run out of expansion room.
Aggressive could be good - Kublai Khan is Aggressive/Creative; Keshiks are pretty good and he starts with hunting which means Scouts to start - though this could actually be bad as popping a religious tech could blow the variant.
The "no friends" issue means few external trade routes. Financial could help out with that - which implies Catherine (who also gets Scouts. . . .).....and

Holy cow: look at those Cossacks

never really looked at their stats before. Ouch.
I think that is my very short list of preferences: Catherine, Louis XIV, and Kublai Khan.
Others worthy of consideration: Napoleon (Agg/Ind) and Elizabeth (Phil/Fin). Despite my objsctions to Expansive, both Cyrus and Caeser would be good for a grow early/ rush early bid.