Benitez is the obvious option but I can see AVB doing well also even tho I dont rate him, I think he brought Mata to Chelsea.
i dont think mata to chelsea had anything to do with avb, it was pointed out in the summer that mata was ready to leave for another club liverpool wanted him but the opted for downing instead. i think it was solely on who was willing to spend the money to get him. Chelsea sructure is different in regards to getting players, they have their finanicial foundation that always have some influence on players. a team like arsenal and tottenham you could say the coaches lead players there.
as for who would compete in the transfer market i would give rafa the edge. And i would give him the edge in working with the current crop of players to compete.