1. Kinda unoriginal, but I do really like the Trojan war. #TeamAgamemnon
2. I'd say Apollo, as he's the god of all the things. Seriously, he's the god of the sun, music, divination, the plague, wisdom, etc.
3. Odysseus, he's more of a brainy kind of hero, as opposed to for example Achilles. I also totally didn't rip off the Odyssey for one of my stories...
4. Don't really have a favourite one, but the hydra, maybe? I mean, if hypothetically speaking I was conquering the world, I'd definitely choose the hydra, what with the nearly unkillable unless you get close enough to decapitate and cauterise the wound and all.
5. I'd say the dragon of Ares, that Cadmus fought near Thebes. It's a son of Ares and its teeth turn into helpful soldiers that you can use to found a city.