"What kind of vice president are you going to be?" Lesley Stahl asked Indiana Governor Mike Pence in his first interview with Donald Trump since Trump selected Pence as his presidential running mate. (Clip in player, above.)

Trump was the first to answer. "I would like somebody who is active," says Trump. "I would like somebody that can go out and really do it," as well as somebody well known in Washington, DC, and well liked by the Republican leadership. And on that score, Trump says he has already gotten important party approval for his choice of Pence. "[Speaker of the House] Paul Ryan called me up immediately and said, 'What a great choice,'" Trump says.

As for what Pence says he can bring to the ticket? He tells Stahl that after 12 years in Congress, his ability to "build relationships with people in Washington, DC, I think, will give me an opportunity to help advocate for the agenda of the Trump administration."

"You're both teetotalers." That's one quality that Donald Trump and Mike Pence share, but Lesley Stahl wanted to know what else the presidential running mates have in common.

"Both of our grandfathers immigrated to this country," Pence says. "[And] we were both raised by self-made men who had high standards and held together strong families."

Meeting Trump and his family was an important part of the selection process, Pence says, and as a result he was able to vouch for them to the people of Indiana. "Folks would look at me and say, 'Are they good people?' And I'd say, 'They're really good people.'"

"We are going to get rid of ISIS, big league," Donald Trump tells Lesley Stahl, and Trump's vice presidential choice, Mike Pence, says it can be done.

"We have the capacity in the United States of America to bring force to bear to destroy the enemy so they cannot threaten our allies, or the United States, or inspire attacks in this country," says Pence.

Pence tells Stahl that he came to New York City soon after 9/11 - part of a delegation of members of Congress - and will "never forget that day.... [O]ur nation has been in a struggle with people inspired by radical Islam ... ever since."

Ivanka Trump, Donald Trump's daughter, and other members of Donald Trump's family will be speaking at the upcoming Republican National Convention, "and I think that's going to be interesting," Trump tells Lesley Stahl.

"Some people say your daughter would be your best surrogate," Stahl says. Trump says Ivanka is "a very talented person" and that that some people had even suggested her as his vice presidential running mate, "but Mike [Pence] it is."