i think they should go for louis van gaal.
liverpool's priority should be to get into the champions league as quickly as possible. they need a manager with authority who can whip the team into line quickly and get them playing positive football.
van gaal has won the league with every team he's managed, playing excellent attacking football. different types of teams too - gifted young players at ajax, millionaire brats at barcelona, journeymen & unknowns at AZ, a mix of the three at bayern. he has a gift for seeing the potential in players - as when he helped schweinsteiger to reinvent himself as a central midfielder. his teams work hard and play with brains and enthusiasm.
on the down side, he inevitably falls out with everyone and gets sacked, but by then liverpool could be back in the champions league.
if they appoint a young guy with a brief to "create a dynasty" the odds are he will be sacked early for poor results. managerial dynasties are overrated anyway, what counts is the quality of players in your squad. just get back into the fucking champions league, then take stock.
martinez, AVB etc all have things to recommend them, but none of them have a proven record of success that matches up to van gaal's.