He wasn't a very good leader, but the story of him fiddling while Rome burned was likely started by the Flavian dynasty, which took control of the empire about five years after Nero's death. When the fire started (it lasted over a week!), he was in Antium, then a coastal town south of Rome. He hastened back to organize a relief effort, clean up bodies and debris, and generally restore order. He blamed the Christians for the fire (perhaps because his political enemies were blaming him for it, and he needed a distraction), and they were executed in large numbers by being thrown to the beasts. Rome didn't have the funds to rebuild so Nero devalued the currency, leading to inflation for the first time in Roman history. Nero was quite young (16) when his mother, Agrippina, most likely poisoned Claudius to install her son to the throne. This is an interesting time in Roman history and is well worth research.

The best historical comparison for Trump has always been Mussolini.