Your question seems to lack understanding of some of the details of Portia's situation when she enters the play in Act I, scene ii.
Portia is not given the opportunity to choose her husband herself, rather each suitor who arrives to "win" her as his wife must agree to choose between three caskets, one of which gives the permission to take her as his wife. If the suitor should choose incorrectly, he must vow to remain single. Most of Portia's potential suitors have been frightened off by this caveat. So, it isn't Portia who is to choose her husband at all, but, in an odd fashion, it is her dead father's choice.
There are only three suitors who actually appear in the play (and actually go the distance and choose a casket, vying to win Portia's hand) -- Prince of Morocco, Prince of Arragon and Bassanio. Though she has shown disdain for the other suitors, Portia hints at her interest in Bassanio at the end of Act I, scene ii.
The best way to compare the suitors Morocco and Arragon is by their reasoning in choosing between silver, gold and lead. Morocco reckons that gold is the most valuable of the three and, comparing that to the value of Portia, chooses gold and chooses wrongly. Arragon chooses silver because he "assumes" that he deserves Portia and chooses wrongly.
In Act III, scene ii, Bassanio chooses to go against appearances and choose lead (the winner). He says:
So may the outward shows be least themselves
The world is still deceived with ornament.
He decides to choose "meagre lead," because its "paleness moves [him] more than eloquence." He wins Portia's hand by choosing the leaden casket that holds her picture, not by her decision.
Why Portia chooses Bassanio: Nerissa tells us that Bassanio is a scholar(1.2.113). Therefore, perhaps Bassanio and Portia's cousin Doctor Bellario will be good friends.