Greatest King:
I honestly done't have the best basis here, being that America has been king-free since nutty George III gave way to a George who refused to become "George I" (though counting him, another George in office, and then the third one...well, maybe the third ruler named George in each nation is just a bit off, eh?) ;)
Louis XIV souns interesting, and Henry IV or V makes for a couple good plays by Shakespeare (technically both, can't remember who Prince Hal is, IV or V, I think it's V but don't hold me to that) but honestly...
Henry VIII just sounds like a badass--six wives, tells the Catholic Church to just go to hell, he'll make his own, eats all day and wants sex all night...at some point you just have to laugh at that and see the awesome ass-ness there and go "DAMN!" (Unless you're one of the two lovely ladies who got beheaded, then maybe not.)
Best Queen:
I'll say Queen Elizabeth for allowing for Shakespeare again via patronage, seeing the Spanish Armada beaten. and because she's the only Queen I know of besides a couple Marys and the current one.
Best Emperor:
Marcus Aurelius. It HAS to be a Roman here, I think, and while Augustus--the other choice I'd ponder here--was great, I feel I need to split the "founded the Roman Empire" credit somewhat between he and old Julius Caesar (ALSO in a Shakespeare play...does anyone else see a running theme here...or maybe just a bad running gag?) Marcus Aurelius was actually a pretty benevolent emperor, was a strong one, and wrote philosophy on top of it all, his "Meditations" are still read today, and he's still seen as maybe one of the closer examples of a philosopher king (so there you are, folks who say things would go to pot if any of these philosophers ever DID achieve the aims they wanted or had power...M.A. was awesome.)
Best President:
As far as I'm concerned that title can go to about five different men--Washington, Lincoln, and then first Theodore and then Franklin Roosevelt--and I'd say really there are Seven Presidents MOST would agree on as being The Magnificent Seven--Washington, Jefferson, Lincoln, TR, FDR, and then JFK for the Democrats and Ronald Reagan for the GOP, as often one party deifies one of those figures and vilifies the otehr, and vice versa, but from the Cuban Missile Crisis to taking down the USSR without a "Hot" War both men did great things, from "Ich bin ein Berlinner" to "Mr. Gorbachev, tear down this wall" both men made great speeches, and from the Bay of Pigs to the Iran Contra both made a pretty glaring mistake...still, great leaders, both of them, and generally they round out the Seven.
But who would I want here?
Out of all of them, I think the president who'd be my pick as one I'd LOVE to live under and someone who'd really represent America the best oversees would have to be Theodore Roosevelt...he didn't take ANY flak, stopped a war, in fact, just because he thought it might damage AMERICA'S standing, he was a man of the people, very progressive...Sarah Palin and John McCain can bang on forever about being "mavericks," TR actually WAS ONE, a Republican I as a Democrat would've voted for ten times over, a conservationist, built up the military and sent a message to Europe without following the Reagan/Bush example of over-building or pissing Europe off totally...JFK's a good choice for just relations be he's a bit young and inexperienced, whereas TR's also rather young and yet being a war hero, governor, assemblyman, police commisioner, Vice President, and finally the President he had a TON of experience. Washington, Jefferson, and Lincoln all are wonderful, but I'm not sure if they could work as well in our era, it's jsut so different--just like TR or JFK, especially, might have some trouble in their times--and FDR is a good choice, but I'd like a bit more of that Bull Moose tenacity.
Theodore Roosevelt--THE American Cowboy King, er, President!