As far as all of the various factors for choosing a team, I'd agree with Ray that the manager sets the tone that determines whether players want to come to town. Although a chance for a ring is certainly a major factor.
the marlins netted a huge crop of desirable free agents with a train wreck of a manager- money was the deciding factor. I've heard of players chasing rings, preferring a coast or a home town, going for cash, but I've yet to hear a guy say "I was offered more elsewhere, but I really wanted to play for Joe Madden" maybe for fringe guys with multiple minor league invites, but never from a marquee free agent