It's a moment that highlights the stark differences between how the two presumptive nominees make decisions, with Trump's unfolding like a reality show and Clinton's taking place almost entirely in secret before her expected announcement late next week.
In conversations with nearly two dozen people inside and close to Clinton's orbit, here are five things to watch as her search for a running mate unfolds:
The Virginia senator appeared with Clinton at a rally Thursday in his home state. They were expected to have a private conversation en route to Annandale, after Clinton visited Democratic senators on Capitol Hill, but aides said they ultimately rode in separate vehicles in her motorcade because she had two interviews to do.
In Annandale, Kaine praised Clinton's work on health care and said she'd put children and families first as president, as opposed to Trump, who he said would be a "me-first" president.
"Do you want a trash-talker president or a bridge-builder president?" Kaine said. "That is what's at stake. Donald Trump trash-talks women, he trash-talks people with disabilities. He trash-talks Latinos."
Clinton thanked Kaine as she began her remarks.
"I appreciate so much the leadership he has shown for this state and now he is doing the same in the Congress," Clinton said.
Kaine is mentioned at the top of every single conversation and Clinton believes he could help win Virginia. He's been increasing his outreach to progressive groups in recent weeks, particularly the abortion-rights movement, and may well address that during Thursday's appearance to make them more comfortable with his views.
He has a strong connection to donors from his time as Democratic National Committee chairman. He has a strong ally in current Virginia Gov. Terry McAuliffe, a strong supporter of the Clintons who has been making the case to former President Bill Clinton that Kaine would be a strong pick.
Kaine also speaks fluent Spanish and is a Catholic, both of which are key.
"He's a safe pick, who gets more interesting the more you learn about him," one Democrat close to Clinton said. "He's fiercely loyal and she can trust him."
2. Sherrod Brown
The Ohio senator is said to be "incredibly intriguing" to Clinton. He could help carry Ohio, which is a battleground where she will need help.
Yet he has two strong points against him: His Senate seat would be filled by a Republican and his strong opposition to NAFTA back in the 1990s could simply highlight her support for it. Bill Clinton is also said to be skeptical of him for this reason.
"He's more of a risk," one Democrat close to Clinton said. "She doesn't like to take risks."
3. Cory Booker
The New Jersey senator excites young voters and the old Obama coalition. Clinton likes and trusts his loyalty.
He's been heavily vetted, particularly his time as Newark mayor. It's unclear what that examination found, but it's key to her decision. This may be the biggest unknown variable of her VP pick. If he's clean, she's interested.
Clinton has told people she's willing to lose his New Jersey Senate seat, if it helps add excitement to her ticket and wins the White House. The new campaign discussion of race could also help his chances.
"Do not count him out," one Democrat close to Clinton said. "She loves his story and what it would add to her campaign."
4. Tom Vilsack
The agriculture secretary is seen as the person on the list she can most trust. She has felt a kinship with him since her first presidential bid and values his judgment, intellect and loyalty.
He would be the "safest pick of all," a Democrat close to both Clinton and Vilsack said, but would be far more of a "Plan B pick."
He is strong in rural America and his native Pittsburgh, but doesn't excite the liberal Democratic base. He's seen as the "boring Tim Kaine," another Democrat said, "but one she trusts implicitly."
5. Elizabeth Warren
The Massachusetts senator is intent on defeating Donald Trump and Clinton loves her fiery approach, but she also doesn't truly trust her and "would constantly worry what she's about to say," a friend of Clinton's said.
For these and other reasons, Warren seems to be the most unlikely pick.
"You get the benefit of her without having to pick her," a Democrat close to Clinton said. "So why would she?"