So Italy and Dalmatia were ruled by the Ostrogoths while Hispania and Narbonesis were ruled by the Visigoths, generally speaking there's a negative connotation regarding the Goths as being the ones that ended the Western Roman Empire but how were they as rulers?
There's only so much I can read about other than Theoderic, Theoderic strikes me as not that bad of a dude, he did outlaw intermarriage between the Goths and the Romans however he did emphasize racial harmony and ruled Italy in its most prosperous period since Valentinian in an effort to restore the glory of Rome.
But what about the other rulers? How did the people view the Gothic kings in general?
The thing about the Gothic kingdom, at least in Italy, is that it was rather short-lived. After Theodoric dies there's a brief period of dramatic political uncertainty which Justinian, the emperor in the east, rapidly seizes as an opportunity to invade, occupy, and integrate Italy into his empire: after Theodoric's death in 526, his daughter Amalasunta attempted to rule as regent in the place of her five-year-old son Atalaric. The arrangement didn't last, and through machinations her cousin Theodahad came to rule Italy and Amalasunta was murdered in 535. Emperor Justinian didn't hesitate to seize on the flimsy pretext to reassert imperial dominion over Italy, and between 535 and 554 he would wage three campaigns on the peninsula, by the end of which Italy would be a Roman province once again.
In any case, I wrote about the more social aspects of Theodoric's rule here and this other answer about the fortunes of some of the old senatorial dynasties under Theodoric, which you might be interested in.