JFM, JR and I went to the National Archives this afternoon and started looking through their digital records for pieces of family history. JR found relatives who were here as far back as the 1790s. JFM found his grandfather's draft registration and learned that he'd served in WWI.
I was able to pinpoint several relatives' arrival in the USA in 1870 (naturalized in 1893), 1909, and 1910. I actually met the great-grandparent who got here in 1909; the others had passed before I was born. It was also interesting to see that the relative who'd been listed as Antonio in the 1900 census was "Tony" in the 1920 census; he also dropped the final syllable of his surname to make it more Anglicized. He wasn't the only one, either. Two Giuseppes became Joseph, Lucia became Lucy, Rosa became Rose, Giovanina became Jennie. (And in one census, boy was THAT name butchered by the English-speaking person who recorded the data. Holy cow.)
Armed with a few more birth years and arrival years than I'd had before, I hope I can track down some additional information in the future when I sit down to tackle the non-digital records.