The Prince of Morocco chooses the golden casket. Its riddle reads, "Who chooseth me shall gain what many men desire" When he chooses that casket he believes it will hold an "angel in a golden bed," but instead finds a skull with some paper placed in its eye socket. The inscription says that not everything that glitters is gold, meaning that whoever chose this casket was looking for gain rather than a wife.
Aragon chooses the silver casket, and the note inside alludes to shadows and dreaming. Thus, we can assume that Portia's father had no wish for his daughter to marry a dreamer, and rather wanted a man who lived in real life.
The third casket, chosen by Bassanio is plain and made from lead. Portia's father has pre-judged that the man who would choose this casket would look to the inside....... not the outside, someone who would love his daughter for who she was, not for what he could get as her husband.
Thus, the considerations were as follows;
1) not a fortune hunter
2) someone with his feet on the ground
3) someone who would give in the same way he received..... and was willing to sacrifice.