If you're more worried about the way you're going to look in the audition, maybe you're in it for the wrong reasons. Likewise, if the band judge you more on your looks than your playing, that says a lot about their priorities and how far they're likely to go. I know the "core" genre is very trendy amongst suburban kids and most start their "bands" for popularity or to pull girls. Coincidentally, these popularity-hungry bands also all sound horrible.
As far as what (pop) punk + metalcore sounds like, look up A Day To Remember...easily one of the most popular "core" bands in recent years. I'm spotting a lot more ADTR clones trying to pop up in the scene.
As far as what bass to take, just about anything you've got works. P-bass or a Jazz bass will fit the bill perfectly. Hell, you'll probably even get away with playing a bass with a single volume control. You'll just really need a nice low end. Tone isn't nearly as important in punk or "core" music than in other styles.