in one of my worlds there are possibly two players that may get max contracts if multiple teams go after the same player both offering max contracts how does the player decide which team to play for? does it help to go max from the first cycle? i have heard coaching staff matters? if so is it just the pitching coach? since they are both pitchers or is it the coaching staff as a hole  is there a chance they would flip teams halfway through? would a playoff team from the previous season have any advantage?

I wuld assume players are loking for the best situation for themselves. That would encompass many of the things you mention above. The new update incorpates a loyalty factor if his former team is in the mix.

the former team does not have enough money to sign him.

I believe there are a couple of factors that the player would consider including: coaching staff, ballpark, and a slight loyalty factor given to his current team. But for the most part, hitters are going to favor going to hitter's parks, and pitchers favor going to pitcher's parks.