For rock music, go for...
TETRA-FANG: This is a band made for a tokusatsu show named Kamen Rider KIVA. Its notable feats were their creative use of violins in a rock music, especially in their first song: "Destiny's Play", for sake of the vampiric Kamen Rider. Other notable songs of that band were:
Supernova
Eternity Blood
Innocent Trap
Individual-System
Shout in the Moonlight
Silent Shout
Rainy Rose (their first stunt in singing mellow songs)
Galneryus: For me, this is the Japanese counterpart of "Thursday" in terms of their song titles and themes. Notably named are:
Cause Disarray
The Flame
Mark of the Revolution (?)
As for J-Pop, I now prefer Chiaki Ishikawa (from See-Saw & whether anime or not), Riyu Kosaka (famed also for singing the songs for Sky Girls OVA & Kamen Rider the NEXT), Yui Makino & Mamiko Noto