Pence is from the cuck corridor. German Midwestern niceness doesn't mesh well with Trump's unapologetic pugilistic virility. Pence endorsed Cruz in the primaries, too, so this is a sort of olive branch to those supporters. Pence is a cookie cutter Conservative, Inc pol. He complements Trump's weaknesses among traditional Republicans.
Gingrich is all style and no substance. The number of things--not just political--that he has been wrong about over the years is pretty staggering when they're taken in tandem. I remember a Fox News special he hosted a decade ago about the impending bird flu epidemic (that never materialized). He is also a serial philanderer, far worse of one than Trump ever was.
Chris Christie should never have been taken seriously for the spot. He's a socially moderate Republican from the northeast--in other words, he's Trump's demographic doppelganger. He makes no sense as VP. Attorney general is far more likely.
Among the serious contenders I preferred Sessions by a mile, of course. He's old, physically small, and not charismatic so it's not surprising that he wasn't picked. But he'll be by far Trump's most reliable congressional liaison. A Trump presidency makes him the country's most important and powerful senator.
At least it wasn't a ridiculous affirmative action pick like Condi Rice. The symbolic power of a presidential ticket comprised of two white men shouldn't be dismissed in The Current Year.
The biggest risk Trump is taking with a GOPe-approved figure like Pence is that Pence will face a lot of pressure from the most determined #NeverTrumpers to abandon Trump sometime between now and November, a move that could sabotage Trump's candidacy. Trump wouldn't have had to worry about that from Sessions, Christie, or even Gingrich, but it's a legitimate concern with Pence.
All this is predicated on Pence actually being offered the spot. It's not beyond the realm of possibility that he is testing the waters here just as he has done remarkably effectively with opposition adjectives (low-energy, lyin', crooked).