Welcome

KH is a great faction. You have some of the best infantrymen there are. Your armies should rely on this heavy infanty, with support of cavalry (hammer-anvil tactic...). Alternatives would be mercenaries, but they are quite expensive. You seem to have quite a good start. Greece is quite rich. Build up your economy and raise high taxes if you must. Send a diplomat to everywhere and get trade rights with the AI-Factions. To expand, there are several possibilities for you, since you are quite in the middle of the map. Mikra Asia is extremely rich, it has many mines. But you will have to fight the Seleukids and/or Ptolemaioi, who will field vast armies of makedonian-style Phalangitai. You also could the other direction, and conquer Italy. Italy is very rich too and you will have to fight another faction, whose armies rely on heavy Inf - the Romans.

BTW, for your finances: If always keep the tax-level on "low taxes" until the city has reached 6000 inhabitants, and then raise them. The city will grow faster, and from that point on you get 1. more taxes and 2. can train armies without emptying the city fastly.