A key part of getting the guitar tone on those MP3's is high gain pickups like EMG's. If the guitar has old school humbuckers like PAF's the effect can be approximated by using a distortion pedal. Both is even better. It tightens up the low end and makes the upper mids more focussed. No need for distortion on the pedal, it's working as a tone shaper, mostly as a hpf. If you do some searching you'll find what pedals work best. You may even have one of them already;
I love PAF's and P90's myself, but for that kind of music they won't cut it by themselves. The tone is too bulky.
Another thing is, like some have mentioned, it's better to track with less gain than most kids think is necessary. But they need to play pretty aggressively with their picking hand to get the amp to growl. The kids who're accustomed to using high gain settings usually have trouble making this adjustment. I find that the tone is best when the strings are hit just below the threshold where they start to warble out of tune for aggressive sections of the song. For the really aggressive parts, sometimes it sounds cool in a chaotic way if the strings do warble a bit. Obviously, light gauge strings and low action won't work for this kind of playing.
JCM800's, Dual Rectifiers, Boogie MkIV's, XXX's, 5150's can all work for this kind of music. I can usually capture it all with one 57 or M160, sometimes a Royer 121 mixed with another mic. Neve-style mic preamps always work, but they can sound laid back compared to say, a Trident S80-style preamp which makes the upper midrange focussed and forward in a way that sounds more "modern rock." Plugin limiters can make the midrange more forward on gtr's at mix.
I agree that it's not necessary to have the amp at blinding levels for this style. This isn't Pete Townsend stuff. Pushing the output stage of the amplifier sounds too honky in the midrange for this kind of music. The tone on those MP3's can be had with a moderate volume level from the amp and a high gain setting on the mic preamp.
Needless to say, it's not a true pop punk production until the vocals are completely tuned and every 1/16th note of the drums, bass, gtr's and vocals is quantized to the grid or to a groove and the drums are reinforced with samples.