Republic, please. The ease of transition was due in large part to the period of benign neglect preceding the 7 years' war. Although they were subjects, the British were extremely hands off with the Americas when compared to other colonial holdings. British administrators for the crown had very little power, due in large part to the remoteness of the colonies and the lack of a strong permanent military presence, and much of the actual decision-making and governing was carried out by local representative bodies. By the time the British started demanding that the American colonies pay more taxes to cover the cost of protecting them in the 7 years' war, the colonists had effectively been practicing self government for decades. Also keep in mind that England was by far the most representative contemporary government, and the only reason that the colonists felt a right to representation was because it was guaranteed to them by their status as English subjects. They had a much smaller leap to make than countries like Egypt, and the intelligentsia were obsessed with the Greeks and Romans, so the idea of a Republic as an ideal form of government was never far from their minds.

Also keep in mind that the transition was not all that smooth. Somewhere between 1/3 and 1/2 of colonists did not want to rebel. Washington only staved off a rebellion of his officers through sheer force of will. The Articles of Confederation were an immense failure. The Constitution was drafted in secret by a group of men who had dubious legal authority to rewrite the AoC. The ratification battles were vicious and nearly unsuccessful, and still left major questions unanswered such as the role of the judiciary and a long term solution to slavery. The transition may seem smooth in hindsight, but the early republic only stood due to the immense collective character of the men who founded it and a great deal of luck.