Rufus King knew politics backwards and forewards by the time the Missouri Compromise rolled around. He cut his teeth during the American War for Independence, and he grew up to become a gung-ho Federalist and a friend and ally to many of the Founding Fathers. He did disagree with a few of them, but everything was kept pretty respectful. Dude was a born diplomat.
In fact, it seems like he was destined to deal with tricky disagreements. Lil' Rufus' parents were rich loyalists, but King became a Patriot during the war. This would later make him among the best candidates to represent U.S. interests in Britain after the war.
Also a check in the born negotiator box? He was a lawyer. In 1777 King graduated from a quaint little Massachusetts college called Harvard (heard of it?) and settled in to begin a prosperous law career. This would rapidly lead to a prosperous political career, because nothing screamed "political potential" in early American like knowing your law facts.
In 1783, King was elected to the Massachusetts State Assembly, and was from there elected to be a delegate for Massachusetts at the Continental Congress. He advocated for a stronger central government, which, under the Articles of Confederation wasn't exactly a walk in the park. (The Articles of Confederation were all about limiting big government power—everyone had just escaped rule by a British monarch, after all.)
His first opportunity to rally for strong central government came when he was elected as a delegate for the Constitutional Convention of 1787. And not only that: he also proved himself to be a staunch opponent to the government including any support of slave interests. (Get it, Rufus.)
Despite being a Massachusetts boy, King's first position in the new Federal government was as a Senator for New York. He used this role to support Federalist interest both at home and abroad. He supported an expanded military and navy, the centralized financial plans of Alexander Hamilton, and making nice with the British government through his support of Jay's Treaty in 1794 (this treaty was credited with stalling war with Britain and making trade relations a tad more normal).
On top of this, King used his influence in New York to make $$$: he was, at the time, the richest guy in New York State. If they had penthouses back in the late 18th century, King would have lived in at least a couple of them.
King's role in negotiating Jay's Treaty earned him the prestigious post as Minister to Great Britain. And the guy was good at his job: he defended American interests while making nice with a bunch of British ministers and forming a relationship that would make King the primary liaison between the two countries.
In fact, this relationship proved instrumental in securing the Louisiana Purchase from France. (But no: our boy Rufus is not the reason they call that tasty New Orleans treat a King Cake.)
When King returned he went back to practicing law (and raking in the cash), but he never fully left the political scene. And when the Federalist Party began to fracture in the early 1800s, he ran as the party's vice presidential candidate in 1804 and 1808. Unfortunately, he got a solid beating in the Electoral College.
He stepped back from politics to nurse his wounds until the War of 1812. Even though he was a totally opposed to warhawks James Madison and Henry Clay, the threat of bankruptcy as a result of the war forced King to get back into the political scene.
He was reelected to the New York Senate in 1813, where he used his position to get America back on financial track. King rallied the Federalists and for a few years it looked like they might make a comeback: King, as one of the only Federalists to have avoided the anti-British fever, was the only leader capable of overcoming the entrenched position of the Democratic-Republicans.
Or that was the plan, anyway. In the presidential election of 1816, he was totally trounced yet again.
Despite this, King clung to the dream of a resurgent Federalist party. When the issue of Missouri reared its ugly head in 1819, King saw a chance for redemption. He took up an opposition to Missouri's entrance as a slave state, hoping he might rally Northern abolitionists and provide new fuel for the dying Federalist flame.
Instead, he was stumped (yet again) by the efforts of Henry Clay and his Democratic-Republicans.
He'd finish his political career as minister to Great Britain, and, even though his relations with the government were totally friendly, he didn't end of up getting much done. He retired to New York in 1826, where he died a year later, brokenhearted about the failure of the Federalist Party.