I'm a bit cynical, I think most players take the highest dollar offer.
I'm reasonably sure Boston was not David Price's first pick of destinations. But $217 million overcame that quite nicely.
Last offseason there were reportedly 3 teams bidding on Gerrit Cole: Yankees, Dodgers and Angels. The Dodgers and Angels hung in there at 8 years * 36 mill. The Yankees bumped it to 9 years and won the auction. That's how Cole picked his favorite destination.