Heroes

Buying the best heroes is also pretty important, just like specialization cities. I would prioritize some of them.
S means "Why I don't have this hero yet?"
A means "I must have this hero";
B means "I could pick this one";
C means "I will not pick even if I have enough hero coins."

Agamemnon - S hero. Good for attack and defend with hoplites and archers, and he is cheap. Use him in hoplites nukes and to defend a city in red revolt;
Ajax - A hero. Great for attack with hoplites;
Alexandrios -  B hero. Good for defending with archers. If you are often attacke by Hoplites, Chariots, Manticores and Medusas, he can help a lot;
Andromeda - A heroine. Great for cities development. Use her to upgrade your small cities, and try to cast happiness with her, this will give a good resource bonus;
Apheledes -  C hero. Do you really struggle in researching? There are better options and you will not economize many resources with him. Also the tecnologies don't take too much time to be finished. He is good in a slow world.
Argus - A hero. Good for any naval cities;
Aristotle - S hero. Great to build Light Ship nukes;
Atalanta - S hero. Great to accelerate CS attacks. It's a good idea to send slingers nukes with her;
Chiron - S hero. Great to recruit hoplites in a cheaper and faster way. Use him in hoplite cities;
Christopholus - C hero. Well, he reduces the construction time of all buildings, but will you always have enough resources to put a building in the queue? He is good in a slow world.
Daidalos - A hero. Good in birremes cities;
Deimos - S hero. Use him in slingers nukes;
Democritus - S hero. Great to city development. Use him to upgrade your small cities and never forget to use items in these cities;
Eurybia - A hero. Good for conquest or triremes cities;
Ferkyon - A hero. Great for support cities;
Hector - B hero. Good for slingers nukes;
Helen - B hero. Good for revolt attacks. She can reduce the revol time, which means less support from the enemy;
Heracles - B hero. Good to along with mythical offensive units. I put him in B category, because the favor you gain from him is very small compared to Temple Looting;
Jason - B hero. Great for farming inactive players and good in Manticores nukes;
Leonidas - A hero. Great for defending during red revolt;
Lysippe - S heroine. Great for horsemen nukes;
Medea - S heroine. Very cheap and insane good for slingers nukes;
Melousa - B heroine. Good for Conquest cities with chariots nukes, even though chariots are very expensive;
Odysseus - B hero. Good to support cities with swordsmen and  to defend against slingers nukes;
Orpheus - A hero. Great to expansion in the very beginning. You can gain a lot of advantage doing Victory Possessions;
Pariphaistes - A hero. Good for naval cities;
Pelops - A hero. Great for conquest cities with hoplites and chariots. Also you can use him in hoplites nukes and for defending.
Perseus - B hero. Good for Harpies nukes. He is a B, because you will mostly face regular units. He can be very good in specific situations;
Philoctetes - B hero. Good to recruit archers faster and cheaper;
Rekonos - B hero. Good with islands with -stone;
Telemachos - B hero. Good against slingers nukes. You will defend with more swordsmen;
Terylea - B heroine. Good with islands with -silver;
Themistokles  - A hero. Great for horsemen nukes;
Urephon  - A hero. Good for Manticores nukes;
Ylestres  - B heroine. Good islands with -stone;
Zuretha - S heroine. Great for LS nukes. She will probably die in every attack, but her buff in the Light Ships is really good.