I think you are going to sign players who will help you win, period. If a player's personality/off field conduct is going to affect team chemistry and the way the team plays on the field then that should throw up a red flag, and unfortunately sometimes it's hard to tell about how bringing a player in from the outside will affect the chemistry of a team, esp. a player who has a history of causing problems.
The bottom line is I think they are going to look for quality players who are going to help them win. V-Mart is a prime example. And if a player is becoming more of a hindrance than an asset, it's time to move on. Using the example of Manny, there was always some issues there, but when they reached their breaking point and were effecting the organization negatively, they moved on.