@ganymede Lindsey Stirling is one of my favorite artists to toss onto youtube.
I fell in love with Yoko Kanno due to Macross Plus.
I also love Yuki Kajiura. I fell in love with her due to Mai-HiME and Mai-Otome.
ETA: Speaking of covers and Macross Plus: Laura Shigihara's cover of Voices.
She also has covers of tons of other music, and has her original music from video games like Plants vs. Zombies.
Yoko Kanno and the Seatbelts did the Cowboy Bebop soundtrack. While I don't enjoy ALL of them, Real Folk Blues and its extended version count among my favorites. But pretty much anything that anime director does, he invites her. As in Terror in Resonance, for instance.