A very, very interesting character there, and clearly the guys were paying attention to their Gritty Crime Dramas, because they created a pretty good (if appropriately exaggerated in some ways) serial killer. Other than his near-genius level intellect, which is often inaccurately attributed to psychopaths, a lot of what he does can be fitted into an understandable psychological model. So I'm going to start speculating.
Jonathan Donovan likely grew up in a very unstable environment. He might have come from a broken home, or at the very least had abusive or neglectful parents. He grew up without boundaries, guidance or any way to direct his intellect. He never learned how to manage his emotions, particularly his destructive impulses. He was almost certainly exposed to violent and criminal behaviour when he was young, most of which was probably random and without predictable consequence. His own criminal behaviour would probably have started very young, most likely acts of trespass as well as disproportionate and seemingly unprovoked acts of violence, with the latter stopping as he realised that retribution for these acts was more consistent. If he was compelled to attend school, teachers would likely have described him as bright but easily bored and utterly uninterested in applying himself. It is probable that he would have experienced people with addictions during his youth and conceived an idea that he was superior to them, accounting for his addictive personality turning to crime rather than more readily-available street highs.
Growing into adulthood, Jonathan Donovan would have been an intelligent underachiever. He was likely very poor, working a series of menial jobs which he considered to be beneath him and abandoned as soon as he got bored. It is possible that he had a surprisingly broad knowledge base, voraciously gathering knowledge on any subject that took his interest before abandoning them just as quickly, likely in response to feeling overly challenged by the subject matter. Police procedure was likely one of the topics that took his interest, not that he particularly needed it considering the corruption and incompetence of the Rook City PD.
The Maniac Jack crime spree likely began some time before the Rook City PD and the Wraith noticed it, as Jack probably honed his skills breaking into abandoned or unoccupied houses, then graduated to stealing from the poor and disenfranchised before tackling the more secure houses of the wealthy. As well as the adrenaline rush of entering a place he should not be, Jack probably also gained a sense of power and superiority from violating his victims' personal space. Once he began stealing from the rich he probably constructed a series of shallow justifications, possibly implying some kind of political or philosophical agenda, but never took them seriously and never intended to make any kind of genuine point. The press attention likely served to feed his ego and increase the pleasure he gained from committing the crimes, as well as encouraging him to be more bold. He may even have felt a sense of pride at attracting the attention of the Wraith, though this would have come hand in hand with a need to assert his intellectual superiority over her. During this time his violent outbursts likely decreased in frequency but became more intense as a result.
The first Spite killing was, as we know, entirely unplanned but depressingly inevitable. While the substance of the crime changes, the underlying motivation - to assuage his boredom with a brief adrenaline rush and to assert his superiority over his victims - remained the same. On the rare occasions he thought about his actions he may have justified them to himself by characterising his victims as weak or stupid, lacking the ability to protect themselves and therefore deserving whatever he did to them. An examination of his victims over the long term would probably have revealed a trend towards more risky or less vulnerable targets as he sought increasing levels of adrenaline and boosted ego. Had his crimes taken place anywhere other than Rook City, the Wraith and a competent police department would likely have caught him much earlier in his killing spree. In particular, his need to literally have blood on his hands after the murder would have led him to make a mistake sooner or later. It is also probable that he would have got more sloppy as his killings continued, feeling invincible in his sense of superiority over the people hunting him. Fortunately, he was stopped before this happened.
By the time he was imprisoned for the Spite killings, rehabilitation was a practical impossibility for Jack Donovan. At this stage in his life he would be unable to develop a sense of genuine empathy, and his success as a criminal would have cemented the notion in his mind that he could act as he wished and get away with it. It is probable that he justified the Wraith catching him as her 'getting lucky', leading to intense resentment as an 'undeserving' individual received attention that he had become accustomed to receiving. Donovan was probably the kind of criminal who would have a scrapbook of their own press cuttings.
Following his breakout from the Barzakh Wing, Spite's personality remains mostly unchanged. He has finally acquired a chemical addiction, though he probably justifies himself as 'better' than those addicted to street drugs. While killing becomes a physical necessity rather than simply a psychological addiction, there is probably still some element of choice in his victims. In particular, he likely prefers victims whose deaths would shock and upset those who discovered them, especially the Wraith. While killing Eduardo and Sara was obviously a massive deal, realistically Spite would never get over hating the Wraith. He would fantasise extensively about killing her, but deep down would probably be afraid of direct confrontation and seek to avoid it in case she bested him again.
I knew I watched all of those episodes of Criminal Minds for something.