I can help you out with the Trivium sound. One of the most obvious things is active pickups. Matt uses Fishman Fluence Moderns (3 voice), EMG actives would suffice.
For the amp, use an EVH 5150 III. For the cabinet, use a Mesa cab with v30s. An overdrive pedal (Tubescreamer). He doesn’t use a lot of gain on the amp, he relies on the pedals to push the amp instead. Not a lot of bass either, scoop the mids. The Trivium sound has largely been very Metalcore.
Throw in a Green 808, turn down the overdrive to 0, set tone at 5.2 and level to 10. Throw in an EQ and drop a little bit of the 400hz, boost the 820hz a bit, boost 1500hz (just a tiny bit). Throw in a noise gate to tighten things up. Take out a little bit around the 3500hz range as well. Throw in a hi and lo cut at the end to clean things up. To get the more clean Trivium tones, use a Vox AC 30.
Search for “Trivium” by Beggars on the Cloud, I uploaded a preset I quickly built for you. You might need to tweak it to suit your guitar and pickups.