I have to agree with the others that have stated Mark Harrigan.

Iv played him in probably a dozen games and failed his destiny once. Inevitably the second or third portal is to R'lyeh, and I dive in head first and get the nicest encounters ever, maybe loosing one stamina and sanity total. One time I lost a few dollars. Pop out of R'lyeh, seal the portal, become a 4 sanity 7 stamina Investigator. Wander my way through kingsport to become Changed and be a 5 sanity 8 stamina indestructible Mark Harrigan.

Also, he starts with a flamethrower.

Rex Murphy. I just love that he looks like he's in a constant state of paranoia, and the Curse that he starts with is just thematically awesome. It's basically what Lovecraft is all about: a curse that is passed down the family tree due to an ancestor's misdoings. During my game sessions, I usually imagine him whining "Why me?", "Just great!" or "This is depressing." Plus, his clue token ability is very useful and powerful providing that he can escape his curse in the first place.