I think 1998-2000 was when I really started getting into this kind of music. Here are a few albums that come to mind when I try and recall what helped lay down a foundation of the music I listen to today.
Blink-182 - Enema Of The State
Saves The Day - Through Being Cool
Alkaline Trio - Maybe I'll Catch Fire
A New Found Glory - Self-Titled
However the one CD that comes to mind more any others, was
Green Day's 1997 release of Nimrod. Before hearing that kind of music, I was listening to bands like Counting Crows, Wallflowers, Goo Goo Dolls etc. Green Day really opened doors for me when I was young, and no matter how much hate I have in my heart for the terrible music they come out with today, I won't ever forget enjoying Nimrod as much as I did. I remember my mom even put the "Good Riddance" lyrics in my graduation yearbook for the little square thing that was designated to me. It's the only album that literally gives me a lump in my throat whenever I think about it. So thank you Green Day for paving the way, and for all the memories you left me with!