Ares is often depicted with a sword and that might help differentiate him from Athena.
This is not a bad idea. Greece used hoplite warfare as its primary military force which had two main weapons: a spear and the short sword.
The spear could go to Athena as it is more practical, takes advantage of the best tactics of the day, and requires discipline to wield properly. Athena is the Goddess of the better parts of war including strategy and discipline so it makes sense.
Ares gets the short sword because he covers the more brutal parts of war. The short sword requires you to get right in front of your enemies face and drive it right into his gut. It's messier and more brutal. The short sword also doesn't require significant training or a formation.
In D&D terms, Athena would be patron of fighters and magi. Ares would be the god of barbarians.
Hecate is the patron of the dark arts and thus most arcane casters. Athena, as goddess of wisdom and defensive warfare, would be the patron of philosophers and hoplites, especially as the Greek citizen-warriors were generally trained with spear and shield, which I would assume to be Athena's favoured weapons.
"[Spartans] think the god of war will never desert them if they keep him in chains; [just as] in Athens they believe Victory will stay with them forever because she has no wings."
That's the point. Ares was the patron of Sparta. The Spartans kept the statue in chains to show that the spirit of war (which the word Ares translates to) was always in Sparta. Just because the stature is weird doesn't mean they didn't hold him as a patron.
Please re-read my post in full. If you have a primary or secondary source that refers to Ares as patron of Sparta, I'd be very interested to read it. :)
As far as Ares' sword is concerned, I'd recommend the falcata. It's very similar to the Greek kopis, and more devastating than the normal shortsword, which is more like the mundane xiphos.