Becerra or Perez would be the first non-Senator Vice Presidential picks for the Democratic Party since Geraldine Ferraro in 1984 (she was a representative). This was from pressure from the DNC to pick a woman for the pick, including voices like House Speaker Tip O'Neal. Before that, Sargent Shriver in 1972 (who achieved national recognition for implementing and orchestrating many of Lyndon Johnson's Great Society programs like the Peace Corps). And before that, you have to go all the way back to FDR's first vice president, John Nance Garner. His qualifications? He was Speaker of the House.
But that's just for getting the nomination. If you look at the tickets that were actually successful, it turns out that we have not had any Vice President in our history who has not served either as a Senator, house speaker, governor, or some otherwise very important national or international function since at least before the 20th Century (this is where I stopped looking; the only exception is James Sherman, who was merely a representative). And this is a good thing; as I noted earlier, the Vice Presidency is none of the authority of the presidency but almost all of the responsibility. If you cannot see the Vice President becoming the President, then that person is not a worthy Vice President.
So that's why Perez will never be the vice presidential pick. Because it would be historically unprecedented for a person who has never held nothing more than a minor politically appointed office, let alone having never held any kind of elected office at all, to be Vice President of the United States. And that's why I think Elizabeth Warren would be a poor pick, too: she doesn't have any synergy with Hillary Clinton, would disagree with her on the issues she's most likely going to have any leeway on the next four years when the vice president is the one supposed to be brokering these deals, and has no major accomplishments to her name besides making government bigger.
Actually, I did forget one guy who doesn't fit this description.
Let's not talk about him.