Social security benefits

hello!

my name is Lori, my husband, Tyler and I are looking to gain residency in Rome, Italy, and move there.
We are from the United States, and are on Supplemental Security Income.  What is the Italian equivalent to that program, and as only residents not citizens (because neither of us have Italian heritage it would be 10 years BEFORE we could get citizenship.). my husband has to work at home,because of his disability(schizophrenia, among other things.). as residents not citizens, how would we go about getting the equivalent to SSI in italy?

the other question I have is what is a good neighborhood near the vatican city that is also reasonably priced?

and furthermore is there anyone who is fluent in Italian that would be willing to practice conversation with my husband and I? 

thank you to any of you who respond!