I used three and I'll tell you what they are and their pros-cons:

-Skype: very bad service for what it is, talk and listen while you play, it is not made for that. Besides, it hangs easily and in my case, with the computer I use, the League of Legends client launches me and the ping goes up.

-Discord: YES it is done for that, play and communicate while. It offers very good service and is very intuitive. I, in fact, use it. You can add friends, open servers, moderate them ANYWAY (from using a bot to erase messages every time until you play music, etc). It's very good.

-TeamSpeak3: less intuitive than Discord but fulfills. The only negative point is that perhaps without having your own server to play with your friends, the rooms are filled with people, often annoying and irritating that only screams.