If you want to avoid "pop-punk", try listening and learning songs from the "origins" of punk (this could be fun!); the likes of The Sex Pistols, The Clash, The Ramones, (anyone care to name the one's I've missed?).
Checking out some of the bands that influenced your favorite artists is also a good way to get an idea of where they're coming from. It'll also give you an idea of the typical lyrical content and chord progressions.
Saying that, I don't think punk is really something that gets taught or necessarily has a right or wrong way of going about it - it just sort of happens...it's not meant to be slick, it's a reaction to something - in THIS posters opinion (how's that for covering your back? :p).
Don't worry too much about me, ignore me long enough and I'll go away.