If you love opera or just want to try a famous song [aria, one kind of song] be sure to try the "Jewel Song" ie. "Ah! je ris de me voir si belle en ce miroir" [Ah I laugh to see myself so beautiful in this mirror] in French from the Gounod's opera Faust.
It's really easy to enjoy if you want to ease into opera. It's all about knowing what to start with. You can't just hurl yourself into an ocean--you need to practice getting on a little boat and going out before you get on a yacht.
Try Anna Netrebko singing the "Jewel Song" here or here. The main character Marguerite tries on jewels while looking into a mirror in this scene.
Gounod was a famous composer, he wrote his own version of Ave Maria, of which there are many. Try Kimi Skota singing it here [fast forward to about 2:30 to get to it]. Arguably, the Schubert version is most well known [try here for a voice or here for just low, nice strings].