When I was learning English I was advised to learn rap music, i.e. 50 Cent and Eminem, because they talk a lot there. Since I'm a big fan of this style, I can recommend Ассаи и Кrec, Каста, Макс Корж, Кравц, and of course Bulltegrims (aka Вадяра Блюз), Anacondaz, БарДак and Noize MC. )

Some links

https://www.youtube.com/watch?v=doetcW5ykpw

https://www.youtube.com/watch?v=mioEG9tiYX0

https://www.youtube.com/watch?v=DovotVh8qUk

https://www.youtube.com/watch?v=lN8s2UaUz24

https://www.youtube.com/watch?v=uTcu2ZyFT04

https://youtu.be/2WoeU8x3eaU

https://www.youtube.com/watch?v=iEaD38bWwD8

https://www.youtube.com/watch?v=WN81XPJ4upI

This is one of my favorites, the video is amazing as well.

https://www.youtube.com/watch?v=VTzHj-R9McA

Советский Марш！！！

Try Zemphira - all the songs of her

би-2 и чичерина - мой рок-н-ролл - http://www.youtube.com/watch?v=7XiGBWapT14

Has to be Григорий Лепс all the way :). He is such a talented artist. I bought his greatest hits and have listened to it non stop for month. He sings really clear in Russian also, so it helps you to pick up sentences and words.