I'm doing research to write an English paper on wars in history but for some of these early wars I cannot find a specific reason for war to break out or for a state wanting to expand.
Can you elaborate a bit? You say you can't find a specific reason, but where have you looked? We will be better able to help you if you give us that information (as well as other relevant information, such as your background - have you done stuff on ancient history before?)
The Persian Wars were at first a revolt of the (greek) ionian cities against Persian rule. The cities called for help to the other greek cities but only two answered Athens and Eretria. That's why the Persian army landed in Marathon. The son and successor of Darius the Great, Xerxes wanted to finish the work of his father and take a revenge against the defeat of Marathon, so he burned Athens when he took it (enabling the discovery of many archaïc sculpture and the well known classical style of the Akropolis).
The cassus belli of Alexander and the corinthian (hellenic minus Sparta) league against Darius III was to take revenge for the past destructions made by Darius and mainly Xerxes, who played a key role in the construction of the memory of the persian wars as "the very bad guy". As Alexander overthrow the persian power, the persepolis palaces where burned. (The volontary nature and the extend of the damages are somewhat contested by Pierre Briant, one of the leading historian of the Acheamenid empire)
The Peloponnesian wars that took place in between is another consequence of the Persian wars. During Xerxes invasion the hellenic league was founded to fight against the invaders. But the league did not last long after the victory so the Athenians created their own league to control the Aegean sea. But as the time went on Athens centralized the (originaly) Delian League, by moving the tresury of the league from Delos to Athens, and by replacing the ships that the members were obligated to build and maintain by a proportional tribute in gold or silver, enabling the economic boom of the Athenian shipyard. The actual cause of the wars are a series of harsh decision of Athens to control some of the members, who called Sparta for help.