It’s a question that dictated re-signing Brandon League and a question that will dictate everyone else the Dodgers do or don’t sign this winter. In this era of deep-pocketed Dodgers ownership, cost seems to be no object. Determining who is the best player on the market may mean more than determining his asking price.

So who should the Dodgers go after first?

After the top few names, it’s not a particularly deep market. But it’s intriguing.

Josh Hamilton is the sexiest name available, if not a particularly good fit. Zack Greinke is the best starting pitcher available, assuming he can’t strike a deal with the Angels in the next 24 hours, and Ned Colletti wants a top-of-the-rotation starter. Torii Hunter looks less and less likely to be an Angel next season himself, and has said he’d consider playing for the Dodgers. How’s that for a backup center fielder?

Pretend you’re Ned Colletti. Whose agent are you pestering the most?