As you mention, the ranking would be inversely proportional to the probability, which is proportional to the number of hands of given type. In order to encourage you to calculate these yourself, here are the ordered counts (ignoring card order), ignoring (high card):
$$ 4, 44, 78, 144, 264. $$
Note that these are not given in the same order as your list! If your counts turn out differently, it might be my mistake, or you might be double counting (say counting a royal flush as a straight flush and a flush).
A particularly simple way to do the calculation is to go over all $52\cdot 51/2 = 1326$ possible hands and classify them using a computer program. This way you don't even have to think, just program.