The First of the Fallen was introduced to be the iconic Vertigo Comics manifestation Devil, but due to continuity conflicts with Neil Gaiman's use of Lucifer in the The Sandman, an alternate background had to be developed. Instead, he was revealed to be the first being created and the first to be banished to Hell - hence the First of the Fallen.
Neil Gaiman used the character of Lucifer in his Season of Mists storyline for The Sandman. In Gaiman's story, Lucifer was the sole ruler of Hell who decided to give up his position in order to travel the world, with the key to the gates of Hell eventually being returned to the representative of Heaven. Because of this, Ennis made it clear that the First of the Fallen, Satan, was a different character.
The being that would become the First of the Fallen was originally the first created being in the universe, created to be God's companion and the embodiment of His conscience. However, he soon came to believe that God was insane, and as a result was banished from Heaven and cast down to Hell - becoming the first of the many others who would fall. He was joined shortly afterwards by the Second and Third of the Fallen, who the First assumed were beings like him when in truth they were merely very powerful demons. On the basis of his misunderstanding, the First assumes that the Second and Third share his power and that the establishment of a ruling triumvirate is the only way to prevent a disastrous war in Hell. The triumvirate lasts only until the next fourth banishee from Heaven arrives: Lucifer, the most powerful being in existence next to God. However, once Lucifer abdicates, the triumvirate resumed their former positions, and the First regains his former title as Satan.
In his ongoing battle against God, the First became aware of another attempt by Heaven to birth a new Messiah and charged the demon Nergal with preventing it. Nergal succeeded in this by infecting a magician named John Constantine with its blood and blackmailing him into sleeping with the Messiah's intended mother, a pure innocent called Zed. Tainted by Nergal's demon blood, Zed became an unsuitable vessel for the Messiah, and Heaven's plans were defeated. However, the First discovered that Constantine was attempting to get the Messiah born through other means, acting as a surrogate father to the daughter of a plant elemental. Nergal attempted to prevent the birth, but was defeated by Constantine and then killed by the First on his return to Hell.
The First came into contact with John Constantine himself in Ireland, where the demon attended the death of an alcoholic who had sold his soul in exchange for the greatest collection of wine in the world. Constantine was also visiting his friend, trying to find a magical cure for his terminal lung cancer, and delayed the First in claiming the soul by tricking him into drinking holy water. This invoked a clause in the contract allowing the alcoholic's soul to go to heaven because it wasn't collected by midnight. The First decided to exact his revenge on Constantine once his cancer claimed his life - but when he came to claim the soul that was his "by right of insult", he found that Constantine had managed to sell his soul to both the Second and the Third of the Fallen. In order to prevent all out war over who would claim the soul, the triumvirate were forced to cure the magician's cancer and save his life; their meager consolation was to do this in the most painful manner imaginable. This only served to increase the First's lust for revenge against the mortal who had bested him.
Things only went worse as the First discovered that Constantine had a spy in hell, the succubus Ellie. In trying to punish the demon, the First was again bested by Constantine, which invoked an ancient law that a demon bested three times by a mortal would receive their torment instead. The First, being the most powerful being in hell at time, declined to receive Constantine's destined torment, but it didn't improve his disposition towards the magician. The First took this vendetta against Constantine extremely seriously: he once spent twenty years making nightly visits to a priest in an asylum, tormenting him to suicide simply to show Constantine the kind of torment that was awaiting him. The priest was pushed over the brink by hearing the First's confession that he had seen for himself that God was insane and so acted against His will.
The First continued to brood over Constantine, until he discovered the true nature of his "brothers" in the triumvirate. Realising that although they might be powerful, they ultimately shared the weaknesses of other demons, he destroyed them both and set about claiming Constantine's soul. Unfortunately, the whole plot turned out to be a long-con arranged by the magician: the First of the Fallen was killed by the succubus Ellie, wielding a knife made from the remains of the Second and Third of the Fallen. Instead of true death, however, the First was reincarnated as a Greek fisherman named Theo whilst retaining his memories of his previous existence. He grew close to defeating Constantine with the help of a demon named Buer, but although the First was restored to his previous life and position the magician still managed to escape damnation through more sneaky trickery.
The First contented himself with occasionally tormenting Constantine, as the events slowly came into place to give the demon the closest thing to victory over Constantine that he ever achieved. The magician's plotting had left him and his friends with a magical taint that was slowly destroying their lives: the First removed this and saved Constantine's friends - at the price of his immortal soul. Constantine only managed to escape by convincing God to intercede on his behalf, denying the First of the satisfaction of complete victory.
Whilst his desire to obtain revenge on Constantine seemed to be sated, the First still enjoyed the opportunity of causing the magician pain wherever he could. He passed on the opportunity of purchasing Constantine (thinking that he wasn't being given the genuine article) but as a final twist of the knife convinced Cheryl Constantine to volunteer to remain suffering in Hell by taking half of her husband Tony's punishment, after her brother John had successfully arranged her freedom
After that, The First seemed to have lost in Constantine's soul altogether even after John himself successfully rescues his sister's soul from Hell. The First and John even teamed up to get Terry Greaves' soul to Hell, and the former knew some knowledge of what will be John's final fate by the end of the series.
Powers and abilities
Since, the first is the current ruler of Hell, he is the embodiment of sin and evil, and thus has nigh-omnipotent demonic power over it. This allows him to perform feats such as defeating a god with relative ease, beyond-superhuman strength, telekinisis, and omnipresence. The First cannot be truly destroyed, seen when John thought he killed him during the last Ennis' run but the First returned. However, God seems to have control over the First's fate when he falls, but decided he would not destroy him.
During the Rake at the Gates of Hell arc, his presence alone in the world is enough to warp every human mind in creating chaos and bloodshed. He also have a degree of control over the sins of mortal men, seen where he managed to kill a group of fishermen using their own deviousness (Critical Mass).