The monarch should be American. However, there ought to be continuity with our original (British) sovereign, if possible. Therefore, here are two suggestions:
a) the American nearest in blood relation to the House of Hanover. This option has the dual benefit of having one of our own and repairing the breach of the past. Also, such a person might be an "average Joe" who happened to win the lottery of life by merely being related to the Hanovers. This might appeal to the American preference for the long-shot, the under-dog, and the "big chance."
b) a prominent and distinguished American male who will marry the most eligible princess from the houses of either Hanover or Windsor, for the good of the country. (I'd be happy to oblige if absolutely necessary. ;)) Seriously, though, this option has the dual benefit of providing an excellent individual most capable of achieving success and establishing a tie with existing royals.
The "chosen one" (not Obama) needs to be a Christian committed to his religion, Judeo-Christian ethics, classical western virtues, and traditional American liberties rightly construed (freedom of religion, equality before the law, representative government, free markets, etc.).
Finally, there should be a state church that solemnizes official government assemblies in a standard way. The king should be a member of this church and have a function in it appropriate to his national responsibilities. The currently emerging American Anglican Province would be my choice.
What do ya'll think?