The alternatives to Tim Kaine were Evan Bayh and Joe Biden. Biden is gaffe-prone and was a bit of an emotional wreck in 2016, given how his son had just fied. Bayh was too moderate and had a bunch of issues with misuse of public funds as we found out in the 2016 Senate Race which he completely blew.
Kaine was also the safest option given the Senate alternatives. If Obama picked Bayh, Mitch Daniels appoints his replacement. If Obama picked Biden, Mike Castle likely would have taken the Senate Seat. OTL he barely beat Biden, but if it were open it'd be an easy easy pickup.
On the other hand, Kaine stepping aside meant that Lieutenant Governor Bill Bolling, a Republican, succeeded him. Virginia thus had a GOP Governor from 2009 to 2014.
Might Kaine get elected to Senate in 2012 instead of Terry McAuliffe?
Kaine was able to beat Clinton and Sanders because he hit the rights demos. He was able to lock down the south and play well with minority and professional types. HRC was busy trying to play to cosmopolitans, women, and blue-collar voters. Sanders was channeling progressive voters dissatisfied with the Obama years, blue collar types who didn't like Hillary, and people who wanted an "outsider". I'm not really sure Biden or Bayh would be able to thread the needle the way he did.
Who would have been a better person to take down a guy like John Kasich, though? Obama and Hillary has a falling out, or he might have just picked her instead of refusing even to consider her for a Cabinet position. Martin O’Malley maybe? Or Bill de Blasio?
Sanders was unelectable. He was too left-wing for the country and HRC enjoyed the heck out of using him as a foil and ripping him to shreds. Single-payer failed 79-21 on the ballot in Colorado in 2016, and I doubt it'd have gone much better elsewhere.
After Hillary tried to railroad Richardson's Cabinet bid Obama didn't want to have anything to do with her... much to his chagrin as she proceeded to make his life miserable in the Senate - pushing hawkish foreign policy, opposing his trade policy, demanding more funding for border security, demanding a medicare buy-in, etc. I think she'd have had turnout issues, as many Obama loyalists just didn't trust her.
Other than Sanders and Clinton, Senator Warren considered running but opted not to. There was a bit of a draft Jerry Brown campaign, and I think he'd have been able to take Kasich to task: a fiscal tightwad with big ideas from the nation's most progressive state who had served 4 terms as Governor.
Kasich was a very strong candidate, but he was damaged goods after the convention. Kasich and Cruz emerged from the brokered convention with their unity ticket. Trump and his core supporters felt robbed and betrayed ... and Governor Tancredo became his avatar.