Possible Kerry VPs:
Edwards, for very obvious reasons, though he is
now clearly the anti-Kerry candidate. Besides, we lose his senate seat whether or not he wins the nomination.
Gephardt wouldn't add anything to the ticket. Kerry is strong where Gephardt is strong.
Evan Bayh is a strong on paper, though factionalism in the Democratic party might sink his chances. He helps run the strongly centrist DLC, whilst Kerry has one of the most liberal voting records in the Senate. He's a good pick if the DNC chooses a non-southern strategy (which is likely to work if it includes Florida and Arkansas/Tenessee).
I might suggest a counter-pick to Evan Bayh in Blanche Lincoln from Arkansas (my home state). Female, rural, southern, moderate, and charismatic. The Democratic party might lose the senate seat, but that's just the price of doing business.
Clark is a strong pick, but I think of him as more of a top level cabinet pick, ie SecState, SecDef, or NSA. He's not a strong campaigner. He ran on leadership, which isn't as important a consideration for a VP. In that sense, the general might overshadow the senator as a commander.
Basically, Kerry doesn't necessarily need a southerner to be his running mate, though it might help. I don't think the Lt. would take the Gen. to be his running mate for some reason. So what does he need? He needs someone loose. He needs someone who can connect with minority voters. He probably needs someone who can connect with women voters.
No time to talk about Edwards, but suffice it to say that he likely won't pick Kerry.