Really? Well, if you're going to look up the bands, let me tell you my personal favorites for writing music.
Red- Not Alone(#1 fave), Hymn For The Missing(2nd fave), Lost, Already Over, Buried Beneath, Let It Burn, Lie To Me, Pieces, Start Again, and Who We Are.
Trading Yesterday- Shattered(another fave), May I, One Day, and Revolution
The rest of my writing playlist(yes, I have one) is the Titanium cover by Madilyn Bailey, This Song Saved My Life by Simple Plan, Ho Hey by The Lumineers, Rescue Me by Kerrie Roberts, Nothing Left To Say by Imagine Dragons, Radioactive by Imagine Dragons, Everybody Loves Me by OneRepublic, Apologize by OneRepublic, Secrets by OneRepublic, All Fall Down by One Republic, All The Right Moves by OneRepublic, Breakaway by Kelly Clarkson(it actually describes Jack's life very well), Lovesick Fool by The Cab, and Angel With A Shotgun by The Cab.
Quite a few of those were discovered through RotG AMVs(Titanium, Rescue Me, This Song Saved My Life, Angel With A Shotgun, Shattered and Not Alone), which is actually a wonderful place to discover great music.
Also, if you would like to see some of my writing, I have a FF.net account as Luminesyra, my most popular story being Cold Insanity with over 100 reviews. The first eight chapters and on my profile