Harrison would be a good pick, if only because saving him would probably help the Whig Party implement it's economic program, which would have probably discredited the Jacksonian free banking insanity that led to Harrison's election in the first place. A Third Bank of the United States that survives to the present day? Sign me up.
Lincoln surviving would actually be pretty bad, in terms of civil rights and Reconstruction. Lincoln's plan was to be far more conciliatory to the South; somewhere between Johnson and Grant on the issue. He probably would have handled it better than Johnson and then allowed Grant, the radical, to finish up. So maybe not bad, but I'm still leery of how Lincoln's Reconstruction would have worked out for black Americans.
Garfield has some interesting butterflies too. IIRC he was a reformist member of the Republicans and was interested in revisting the civil rights issue. That could mean a lot of changes in the late 19th and early 20th centuries.
McKinley surviving pretty much butterflies away the Progressive movement and allows socialism to take root in the United States.
Harding's survival gives us a second term not much different than Coolidge's. Seriously, I don't see him behaving any differently.
Roosevelt would resign at the end of the war. If was in good enough shape that he didn't need to (a massive POD required here), then he'd probably try and push through his second bill of rights in some form or another. We would have national health insurance if Roosevelt had lived. He'd also probably start some on civil rights, maybe desegregating the military.
Kennedy surviving means no Medicare, no Medicaid, no civil rights legislation, no Great Society. I'll pass on saving Camelot.
Nixon "surviving" means national health care and no repudiation of government.
I'd save FDR, if only because it would mean a smoother transition to Truman and then Roosevelt could go off and try to run the world as head of the UN.