A number of years ago at the Stereophile Show in NY Roger Sanders (Innersound) played his own recordings of amateur singers. An unknown woman was singing "O mio Babbino Caro" and that performance - on the Innersound Electrostatic - is still the greatest experience I have ever had in reproduced music (the Metropolitan Opera is still better though). But the rest of Gianni Schicci is rather boring, so get it on a compilation.
You can buy a number of compilations to start out. I am a great fan of the late Jussi Bjorling ("Operatic Arias" RCA GD85277 and "Duets and Scenes" RCA 7799-2-RG, the latter opens with the Bizet duet mentioned above). The recordings are from the 1950s (Bjorling died in 61), but the beauty of the music survives!
Any of the more most popular operas by Verdi (La Traviata, Rigoletto, Aida) or Puccini (Tosca, Turandot, La Boheme, Madama Butterfly) will give you hours of beatiful music that will touch your heart. I would suggest La Traviata (the opera in Pretty Woman) and Tosca to start with, probably the latest recording from Saltzburg with Anna Netrebko and Villazon in La Traviata (they were sensational in Rigoletta a week ago at the Met) and the incredible Callas recording of Tosca where you get both beauty and an incredible sense of drama between Callas and Toto Gobbi (EMI 77774 71758).
I envy you. You are about to embark on a remarkable journey of discovery.