My first exposure to this genre was when I moved back to Houston in 2002. I was into metal pretty hard back then, Hatebreed was a new band at the time that was really on the rise. I went to a tiny nightclub to see them with Six Feet Under, who was one of my favorite "Death Metal" bands at the time. The whole show was bat shit crazy. A local band called Will To Live opened the show and really killed it, they are the GOAT Hardcore band from Houston but they never really had much success outside of H-Town(they got old around the time they started to breakthrough).
The second band that played that night was a really great hardcore band called Death Threat. They tore the house down. They have some great stuff that I would recommend.
That same night was the first time I seen Shadows Fall, young and hungry 2002 Shadows Fall they totally stole the show that night. The whole crowd was dead for Six Feet Under, I couldn't believe it, Hardcore kids don't like any other subgenre apparently. Hatebreed closed the show with a great set. Really fun concert, one of the favorites I've ever been to. Craziest crowd ever.
After that concert I really got into hardcore and I still like it a lot. Madball, Earth Crisis, Minor Threat, great stuff.