Well..for MCR they dont have a distinctive sound.Its your typical punk rock sound, lots of distortion.
But their lead guitarist, Ray Toro, has a quite sweet sound. He uses LOTS of LP's, all mostly Epi Elitist, and Gibsons.

The LP standard you're getting may get you close to MCR's tone.
But one thing....CREATE your own. You dont wanna be playing using that same tone all day long..

Play around with the EQ .

Then...go to ishibashi, get one of those Fernandes / Burny.
They're made in Japan.

Probably costs you around 70k Yen, about...2kRM?