Why does Bassanio set his sights on Portia?
Who knows. This answer will depend on who you ask. Some readers can claim it is because he genuinely loves her while others will claim that he's after a rich sugar mamma.
I'll start with actual love. On a previous trip, Bassanio saw Portia and supposedly fell in love with her. And why not fall in love with her? She's rich and super attractive.
"In Belmont is a lady richly left, / And she is fair"
I'll support true love and love at first sight. It's not like Shakespeare hasn't ever written about that before (I'm talking to you, Romeo and Juliet).
It's also possible that Bassanio has his sights set on Portia because so does everybody else.
"Nor is the wide world ignorant of her worth, / For the four winds blow in from every coast / Renownèd suitors"
That quote is basically saying that a whole bunch of men are attempting to win her heart and pass her father's casket choosing game. That makes Portia a prize to be won. A lot of men like competition and hate losing. Bassanio might be attracted to her and winning her and her wealth would be totally awesome. If you think that's impossible and think that kind of thing doesn't happen, I suggest you watch an entire season of "The Bachelor" or "The Bachelorette."
The last possibility for Bassanio setting his sights on Portia is that she is rich and available. He's clearly not good with money. It's why he has to borrow more of it from Antonio. Perhaps Bassanio simply wants Portia because she can financially provide for him. The fact that she's available and attractive are bonuses.
He likes Portia because she has inherited riches, has wonderful personality traits and virtues. He is obviously fascinated with her riches in that this would help him settle his many debts. He compares her to the historical Portia who was the daughter of Cato and wife of Brutus and was absolutely beautiful. He has many other suitors standing in his way so he feels like he will have to borrow some money and pretend to be rich so that he might impress Portia!