The Acropolis is a flat-topped rock that served as the ancient citadel, and the buildings on it went up when Athens was at its richest, in the 5th century BC. Everything you have seen in photographs sits up there close together, so the visit works as one loop.
Go early rather than late. The plateau is exposed, the marble throws heat back at you by midday, and the paths narrow wherever everyone stops for the same view. The guided city tour runs in the morning for that reason and takes about five hours with the museum. If you want it arranged, an Athens tour covers the hill, the museum and the entrance fees with a licensed guide.

The Propylaea and the Temple of Athena Nike
The Propylaea is the gateway you walk through, and it controls how you enter the plateau. Stand in it for a minute and look back down at the city before you pass, because that framing is what the building was for.
To one side sits the Temple of Athena Nike, small enough to walk straight past while you look at the Parthenon. Slow down long enough to actually see it.
The Parthenon
The Parthenon takes the far end and takes the crowd with it. Walk the outside first, all four sides, because the columns lean and swell in ways that photographs flatten. Then look up at the metopes, the panels above the columns, and the pediments at each end. The sculpture that filled the building is in the museum below, which is why the order matters.

The Erechtheion and the Porch of Maidens
The Erechtheion is the strange one, and its Porch of Maidens carries carved women in place of columns. Most people give it ten minutes and the Parthenon an hour, and I would turn that around and give the porch the time.
The Acropolis Museum After
Come down and follow the walk past the Herodion and the Theater of Dionysos, then go into the museum. The new building holds the votives, the objects of everyday life, the statues from the archaic period and the Caryatids, and the Parthenon hall with its metopes, pediments and frieze is the room the building was designed around.
Which comes first, the hill or the museum? The hill, and the order is the whole argument: the rooms are full of things made for the buildings you just stood in.