1) At the start, my KH full stack armies look something like:
-1 or 2 FM
-4 Hoplitai (Classical Hoplites)
-2 Thureophoroi
-2 Ekdromi Hoplitai (Light Hoplites) or 2 Thorakitai Hoplite (Greek Hoplite Phalanx)
-2 Toxotai/ Toxotai Kretikoi
-2 Sphendonetai/ Rhodoi Sphendonetai
-2 Lonchophoroi Hippeis
-2 Hippeis / Hippakontistai
-2 Units of whatever I feel I would need the most depending what'll be the objective of the army (if it will siege a settlement, 2 artillery pieces), the composition of the enemy stack, etc.

Later in the game:
-2 Koinon Hellenon Phalangitai (Koinon Hellenon Phalanx)
-2 Epilektoi Hoplitai (Greek Distinguished Hoplites)
-2 Spartiatai Hoplitai (Spartans Hoplites)
-2 Thorakitai
-2 Misthophoroi Thraikioi Peltastai (Mercenary Thracian Peltast)
-2 Toxotai Kretikoi or Bosphoran Archers or Caucasian Archers
-2 Sphendonetai Rhodoi
-2 Prodromoi (Successor Medium Cavalry) or Lonchophoroi Hippeis
-2 Skuda Baexdzhyntae (Schytian Raiders)
-2 Hippeis Thessalikoi / 2 Xystophoroi

However, as Titus Marcellus Scato pointed out, the Greeks depend much on regional troops, because you won't be able to retrain many of your best troops in several regions. An example, you can swap Spartan Hoplites for Galatian or Thracian Swordsmen.

2) My first objective is to control the triangle that goes from Sparte to Dalminion to Kallatis. Which means, your first objective is to defeat the Epirotes and Makedons, and leave them with a single settlement in Italy and Mytilene respectively (if they accept ceasefire and trade rights after this, great). Later, war with the Getai will follow. After that, the Sauromatae and Arche Seleukeia await. You could try to achieve your objectives with naval invasions on your target cities bypassing land battles, but I don't like to play KH that way.