What was the criteria that Portia's father demanded for the hand of his daughters?
Portia's father seems to have anticipated that young Portia would be the target of gold digging suitors upon his death. Young and in possession of land and wealth, Portia is vulnerable to men who may mislead her regarding marriage, and her father wants his "will" to exert upon potential suitors his own preference that a man worthy of Portia win her hand and inheritance.
Young women rarely would choose their own husband, and Portia is no different in this. Unlike Juliet and Rosalind, she abides by her father's decision to marry the man who succeeds in the casket game, a choice among a gold, silver and lead box.
While Portia does seem to abide by her father's will, she also seems to "bend" his will to hers.
While the first suitor leaves disappointed in his wrong choice, we find that Portia seems to add an extra condition when Arragon tests his luck. Here we see that the additional stipulation is that he may have to forego marriage to anyone should he fail with Portia:
I am enjoined by oath to observe three things:First, never to unfold to any oneWhich casket ’twas I chose; next, if I failOf the right casket, never in my lifeTo woo a maid in way of marriage; lastly,If I do fail in fortune of my choice,Immediately to leave you and be gone.
the terms of her late father’s will. They state that whoever seeks to marry Portia must solve the riddle of the three caskets—one gold, one silver, one lead, each with an inscription—or, failing in the attempt, agree to remain a bachelor for the rest of his days.
The criteria demanded by Portia's father was as follows. To choose the correct casket without any help or clues from anyone else and if unsuccessful you must leave Belmont and never try for Portia's hand in marriage.