In The Taming of the Shrew, how does Petruchio's first meeting with Baptista set the style of the courtship? What kind of father is Baptista?

Well, Petruchio's tactic, here as elsewhere, is to divorce his words from the real action of the play, just as he does to Kate in the taming scene. Here's his opening line:

PET:
Pray, have you not a daughter
Call'd Katherina, fair and virtuous?

BAP:
I have a daughter, sir, called Katherina.

Petruchio is happy to pretend that The Paduans are obsessed with gossip and reports (the reason Baptista marries Bianca off to "Lucentio" is because he's heard "reports" that Vincentio is very rich) and Petruchio knows how to get Baptista to agree. (1) - emphasise the GOSSIP that he's heard, and (2) agree to marry KATHARINA who he already knows that Baptista wants to get rid of:

You wrong me, Signior Gremio: give me leave.
I am a gentleman of Verona, sir,
That, hearing of her beauty and her wit,
Her affability and bashful modesty,
Her wondrous qualities and mild behavior,
Am bold to show myself a forward guest
Within your house, to make mine eye the witness
Of that report which I so oft have heard.

As for Baptista as a father, he doesn't come off too well. He'd be happy to marry her off to anyone, if only he thought she'd agree:

You're welcome, sir; and he, for your good sake.
But for my daughter Katherine, this I know,
She is not for your turn, the more my grief.

He calls Katharina, to her face, earlier in the scene a "hilding of a devilish spirit". He treats her as a commodity to be gotten off the shelf - as fast as possible. Let's just say he's not up for father of the year.