The categorisation cannot be clean cut, because it mixes forms of government with sizes, which is related to how heterogeneous they were. Taking what they were for the most time (Macedonia was an Empire for a very few years):
Tribes: Britons, Gauls, Iberians, Germans.
City-states: Athenians, Spartans, Thebans.
Republics: Romans, Carthaginians.
Kingdoms: Macedonians, Ptolemies, Kushites.
Empires: Seleucids, Persians, Mauryans, Han.