I am just wondering about when it became common practice for prominent Roman generals/politicians to put their faces on coins that they minted? I know that under the emperors this became common practice and that Sulla did this during the Civil Wars, but was anyone else doing this at an earlier time?
Lydia, the first to start making coins, did so for about 600bc but they did not depicted people, famously a lion. Then in Ancient Greece, 479 b.c. King Gelon of Syracuse issued a coin called a Demareteion with a portrait of the Demarete, it is the coin to first feature a head of a person. Another Greek coin from 440 b.c., the most renowned ancient coin, is the Athena's Owl. A silver tetradrachm with Athena's head on the obverse(front) and her sacred owl on the reverse. Many Greek coins were issued with the heads of their gods and goddess, actual people were rarely used. Even Alexander the Great did not have his image on his own coins(after his death, some coins were made with his image).
In the Roman Empire, probably 99% of emperors had their head on some denomination. Augustus was on at least 20 different coins: Nero had reached at least 14. Almost every Roman coin from 180 b.c. to the fall and into Byzantine had at least one side with someone's head.
TL;DR Lydia was first used coins but did not have people on them, Greek coins would often have a gods head and then in the Roman Empire almost every coin had some real persons head.