Kasich is of moderate temperament, but his politics are very right wing. If Clinton wants a Republican, she’ll go for a genuine moderate. And there aren’t any Republican moderates anymore with real stature who aren’t ancient. Well, there is one who is ancient, but would work well: Colin Powell.
My predictions:
Clinton/Wes Clark- Clinton values loyalty and someone who shares her worldview. Wes Clark is perfect and adds value to the ticket. He’s popular with Democrats and moderates.
Rubio/Tim Scott-Scott’s well timed endorsement plus the appeal of a young, multicultural ticket will be hard to resist.
Cruz/Rand Paul- Cruz will have trouble getting anyone to join his Goldwateresque ticket. Paul shares Cruz’s anti establishment attitude, although they are not ideologically the same.
Trump/Carson-Trump is more likely just going to handpick someone he likes that we’ve never heard of, but of known national figures Carson makes the most sense for a guy like Trump. Trump could also grab Allen West, or perhaps a right-wing general like Anthony Zinni or Hugh Shelton.
Kasich/Rubio- If Kasich pulls it off, he doesn’t need experience to balance the ticket, he needs youth. Rubio is jjust so obvious.
Christie/Walker- Two governors are fighters, plus Christie needs to get the base excited since they’ll be “meh” over his nomination. The base loves Walker, and frankly Walker’s exit was premature.
Bush/Condi Rice- The Bushes, like the Clintons, value loyalty, and Rice is loyal, serving both Bushes and will probably serve a third if she gets the chance.
Since VP picks are one in a hundred type deals, don’t count these as predictions, just best guesses. For each VP possibility I named, there are plenty of other candidates for each potential nominee who can give them what they are looking for.