Nobody has said this yet, but I"m going to go with Roscoe Conkling. He was young and very charismatic, with a talent for machine politics. He was a protege of Lincoln while also being a Radical Republican. At the time, his name was not synonymous with Gilded Age corruption. If Lincoln lives, I think Conkling cinches the 1868 RNC.
I also doubt Grant enters politics if Andrew Johnson is never President. People forget just to what extreme lengths Johnson had to go before Grant even considered a Presidential run against him. He literally had to semi-coerce Grant into committing a crime that could've landed him in prison for five years before Grant turned on the President. The other thing I really doubt is the Lincoln impeachment hypothesis. Lincoln's main clash with the Radicals was the fact that they kept making moves that could've made a tenuous position in the border states (keep in mind, Washington D.C. is sandwiched between a border state and the Confederacy) outright catastrophic with early moves toward abolition. Later on, it was over Wade-Davis and the Radicals' plans to disenfranchise the white south, as well as undermine the Union's reunification.
I don't see why Lincoln would give the Radicals grief on issues like civil rights. Hell, I'd bet he would actively scheme and arm-twist to pass the 14th and 15th Amendments, nor do I imagine him being particularly lenient towards violent Redeemers. Lincoln's last public speech (the one that caused John Wilkes Booth to vow "now I'll put him through!") was him defending his conduct in re-admitting Louisiana without a black suffrage clause, not because he was opposed to black suffrage, but because working to attain it within the present system made more sense to him.
Also, Lincoln was just clever. Andrew Johnson was a famously inept and obstinate President who needlessly wounded his own position because of his spiteful personality. Lincoln can certainly connive to avoid impeachment if it comes to that. But why would it? He won the war, liberated the slaves, and is probably working towards black suffrage. In the euphoria following triumph, I don't see the Radicals making an almost certainly fruitless move to impeach him. Who would they impeach him for? Vice President Johnson? Would they impeach him too? If it was tenuous that they could get Johnson ousted in favor of Wade, how on earth could they hope to get Lincoln ousted in favor of Wade?