The story of Madrid goes likes. They ALWAYS feel they have to win everything, and on top of that they HAVE to play beautiful football. Capello had 2 seasons in RM, and got them both times the league title. Still they sacked him, because it was no beautiful football, effective yes.
As for the coach its hard to say. He has no decision in buying players. He may have his opinion. Lets say, he needs a striker, and they will get him the best striker available in the world, regardless if it fits his tactic. Thats what Florentino Perez, Jorge Valdano and Miguel Pardeza do. They are responsible for buying the players. This season when they bought so many players, Pellegrini had to inevitabily to discard some of the existing players, and RM had a difficult task to sell all the players, and sold them pretty badly (Sneijder, Robben, Javi Garcia, Negredo, etc.
What will they get? A coach with good reputation, that they can manipulate one way or the other.
What should they get? A coach with high character, outspoken, that speaks his mind, and that has the personality to manage a squad filled with world class players and their ego´s.
P.S. I think this was Guti´s and Raul last season there. Pellegrini had tremendous guts to bench them through the whole season.