Hi! I'm 2nd/3rd generation American

Hi! I'm 2nd/3rd generation American with ancestry from Italy and am looking to become a duel citizen. I have some slight problems though, into looking to see if I am eligible as my Italian-born grandparents were born around 1907, and on the other side a little bit later. Understandably, they have died before I was born or when I was a kid (at age 90). I know there's a few loopholes, as my great-grandfather become a citizen, and so his wife (my great grandmother) automatically did too, making me (and my parents) inegible. What is the easiest way for me to see who is a citizen and who didn't become a citizen without spending much money? I've tried Ancestry, and little to none of the official records are on there that I would need for this.. Thank you!