Those are our options when we ask the question, who would be the current ruler of the United States had George Washington accepted the offer to be king (ceteris paribus)? An article in Ancestry Magazine from last September (h/t Slate) tries to figure out exactly where we would be now. Slogging through the different types of primogeniture (agnatic, cognatic, agnatic-cognatic) and having to decide at the start whether to go to Washington's elder half-brother (Augustine) or his younger full brother (Samuel), the authors end up trying them all out.
The funny thing is that the claimants, Frank, Brynda, and Paul, probably have no idea that they could be sitting in the White House (or, perhaps it would still be called the "President's Palace"), waving ceremonially, while the Congress, consisting of a Prime Minister leading the executive and legislative branches, argues over a bill on the floor.
What a world it might have been!