An oil painting hung above the fireplace says sophistication. But, a gentleman must exercise prudence when selecting his artwork. It will serve as the room’s focal point and speak volumes about its exhibitor. 
It should be a portrait.  Frankly, the mantle is no place for a painting of a wheat field or a unicorn (unless mounted by a king/prince/general in full military regalia). The portrait should convey power and confidence while embracing its own whimsy.  You want visitors to grasp instantly that you are a formidable man endowed with great intellect, humor and humility.

Some gentlemen will opt for a self-portrait.  Done well, this can triumph superbly, but executed poorly, you may broadcast a message of ego and arrogance.  Remember, no one likes someone who takes himself too seriously.  Those opting for self-portraits should go for quirky or screwball.  Consider, for your fireplace mantle, a depiction of you with velvet smoking jacket and pipe seated on a tufted brown leather chair next to that same fireplace. Or, what about you posing stiffly and expressionless with your animal companion, preferably a cat?

We at G@H prefer portraits of historical personalities. With self-aggrandizement concerns eluded, you are free to be more subtle and ironic in your selection.  Sources abound.  Wikipedia Commons maintains a library of portrait paintings (click here), many of which are in the public domain.  Wikipedia also has a gallery of official Presidential portraits (click here).  While JFK claims the most iconic portrait, we prefer that of William Howard Taft. No one brings more gravitas to your fireplace mantel than the gluttonous Taft, the only President to have served in all three branches of the federal government.