This woman has a lot of videos of her singing Armenian songs on YouTube: https://www.youtube.com/watch?v=7itoPIgeXH0&list=PL3iIpV1t3n-jBJjMj1VVbe0cBPqMgLA5x

I'm not sure what songs are popular in Armenia right now, but I can think of several Armenian songs that might help you learn more of the Armenian language. For example, Sirusho singing "Havatum em" ("I believe"), Ruben Haxverdyan and Sirusho singing "Mer Siro Ashun@" (I think it means "Autumn of our Love" or "Our Autumn Love" - sorry, not sure), Sirusho and Sofi Mkheyan singing "Arjani e" ("Is Worthy"), (okay, no more Sirusho ones, I promise) Lilit Karapetyan: "Zhamanakin," "Aghotkh Zinvorin," "Patmutyun," etc..., also look up Vardan Sargsyan, Olga Ayvazyan, etc.... Actually, there is some website regarding popular Armenian music - something like Armenian Music is the Best - you might want to look it up.