Pence

Assuming this checks out, it would be a rare case of the Trump campaign doing something right.

The key to understanding vice presidential picks from a political standpoint is that the only substantial possible effects are downside ones. There’s no evidence that vice presidential choices can attract a non-negligible number of voters to the ticket; even the vaunted home-state effect only seems to apply in states to small to tip the Electoral College except in an extreme case. A bad pick, like Palin or Eagleton, can hurt you but nobody can really help you.

Newt Gingrich — an undisciplined campaigner with a lot of personal baggage — is exactly what you don’t want. (And even if you assume that VP picks have a potential upside too subtle for political science to pick up, I don’t know what story you could tell that Gingrich has anything to offer there.) Pence, a safe, boring pol is exactly what you’re looking for.