Purely as a mental exercise, I wonder if Aegon IV was the absolute worst Targaryen king...easily "among the worst".
Half-insane sons who didn't actually rule (i.e. Aerion Brightflame) don't count here.
By my count there were basically five outright "bad" Targaryen kings: Aenys I, Aegon II, Aegon IV, Aerys I, Aerys II. That is, who people within Westeros would dislike: the point has been made that Daeron was a general but not a governor, while Baelor was popular with the smallfolk but a delusional zealot, but they at least had their positive sides and people wouldn't outright "hate" them. Even Maegor the Cruel could be said to have been an "effective" king. Absolute "worst" king is a mix of "cruel" with "absurdly incompetent", i.e. not just a vicious king or an idiot king, but a vicious idiot king.
Well, similarly, Aenys I and Aerys I weren't too terrible: they were weaklings who weren't effective at rule (Aerys I was practically an absentee king), but at least this was mostly inaction: they didn't outright create problems.
So I think the short list for "Worst Targaryen King ever" can be narrowed down to Aegon II, Aegon IV, and Aerys II.
Aegon II barely ruled for two years, and nearly half of the Seven Kingdoms never acknowledged his rule during the Dance of the Dragons. From what we've been told, he was a complete slimeball, and hot blooded moron. ANY mention of positive action he takes in The Princess and the Queen, i.e. not initially wanting to usurp the throne until his mother goaded him into it, was stated by GRRM to be just propaganda by Aegon II supporters. And that's just a civil war - he didn't exactly introduce solid domestic policies during a brief reign consumed by civil war. Aegon II's an odd case because he isn't so much as "bad king" but really a question of "can we even call such a short-lived usurper a 'king', strictly speaking?"
Aegon IV, meanwhile, succeeded to the throne without dispute and ruled for 12 full years. Obviously, on a personal level the man was a glutton and buffoon, and may not have had an outright reign of terror, but certainly was a vain, petty man. Needlessly causing so much strife at court that it's a wonder they didn't actually turn to open civil war (and given that the Blackfyre Rebellion immediately followed his death, that may have capitalized on a lot of anti-royal court anger, though also said to be combined with anti-Dornish attitudes). Of course his biggest and worst mistake was the sheer number of mistresses and bastards he had over the years, which in a hereditary monarchy is a recipe for disaster. Viserys I is in no way comparable: his first queen died, he later remarried, and his daughter from his first marriage later came into conflict with his son from the second. Otherwise Viserys I was a sound ruler and did exact oaths of loyalty to his daughter (her enemies just ignored them after he died).
Aerys II is of course the one that broke the whole dynasty, through outright madness. Even Aegon IV was never crazy enough to outright execute high lords purely on a whim, and burn large numbers of people to death while at court. On the other hand he had a long reign in which the realm prospered - because his Hand of the King increasingly ruled in his stead.