The short answer
Good news first. Argentina sits inside the Hague Convention, so an apostille is the right and sufficient stamp for a paper used there. Nothing further is needed at a consulate afterwards. That is the biggest saving on this route, in both money and days. What is left is picking the correct counter here and getting the sheet itself right.
Since 1988, and what it changed
Argentina came into the Convention in 1988, and this country had already joined in 1978. The Convention text itself was concluded in 1961. Before a state joins, paper has to pass along a chain of offices ending at a mission. After it joins, one stamp stands in for that whole chain. So a sheet stamped here arrives already vouched for.
Which counter signs it here
Two offices share the work in this province. The Prefettura takes administrative papers: registry extracts, school reports, health sheets, police records. The Procura della Repubblica takes judicial and notarial acts, so a court ruling or a deed signed before a notary belongs there. The apostille requirements for Argentina do not shift that split, because it follows the paper in your hand and never the destination. Bring the wrong sheet to the wrong desk and you lose a morning.
Family files across the Atlantic
Puglia sent a great many families to Argentina, and the paperwork still runs in both directions. People here order records from there for a citizenship file, while people there ask for birth, marriage and death records held in towns near this city. Ask what document legalisation for Argentina the receiving registry wants, because a consulate, a court and a provincial registry each keep their own habits.
Cost and spare originals
At the counter the cost is a €16 tax stamp for each sheet, with some papers exempt. Nothing else is charged there. No waiting time is published, so leave room for a second visit if the queue is long. Order two sealed originals where the issuing office allows it, and keep one at home. On an apostille from Italy to Argentina a replacement means starting at the town hall again.
Translation, then delivery
The stamp covers the signature and the seal, not the words. Most readers there will want the text turned over before they file it, so confirm the required language with the receiving office in writing. Our translator then swears the text before a court here, which puts the wording on oath. Send the sworn text stapled to the stamped original, and keep a scan of both.