I would very much like to meet and shake the hand of President Lincoln, because he tried to make way for equality among people and he kept our states "united".
If I could pick more than one, I'd also like to shake the hand of the Rev. Dr. Martin Luther King, Jr. for the very same reason. (He might get a hug, too.)
Then, there'd be our founding fathers and mothers who contributed to creation of our constitution, declaration of independence, and are basically the reason we're here today. I respect Jefferson the most, but Washington actually (despite the fact that he kept slaves--GRRRRR--though he freed them after his wife died) was very honorable, too: he was offerred kingship of our country because of his success in the battlefields, but instead he chose (temporary) presidency and established the rotating schedule of presidents and congress and senator members similar to what we have today to ensure that no single person could affect the country or parts of the country for too long and become oppressive (like the lands from which most Americans of the time had fled in Europe and elsewhere). Washington was VERY honorable in doing such, in my opinion. I suppose it would be inappropriate to shake his hand, so I would settle for a deep curtsey.
And finally (though I'm missing many) I'd drop in on Mr. Isaac Newton, scientist, philosopher, statesman, "man-about-town" a-hem (okay, so he wasn't PERFECT)... He sounds like a nice, crazy-brilliant geek that I'd like to hang out with some afternoon, perhaps flying a kite in a storm or napping under an apple tree...
Of each of these people I would probably ask no questions--I would be in too much awe in their presence (except Newton: I'd ask him what was that over there, boiling over on his laboratory table while he greeted me).