First, I wouldn't advise getting any sort of equipment if you don't plan on using it frequently and with purpose, you'll just kick yourself later as it sits around getting dusty. Also, you'd have to invest in more than just a mic to get quality thats noticably better than you're getting with your Rock Band mic. At the minimum you'd need a mic and a decent interface with some sort of Pre-amp. The Presonus Firebox is something I've used for years and had pretty good results.
If you're just trying to do vocal covers I'd just try and bum from friends if you know any that are into home recording, it takes some sacrifice even at the most basic stages.
In the end though, I'd stick with a cheap Cardioid mic over something meant to cover all of your bases. It's really difficult to get good/full instrument tone on a budget anyway, I'd suggest investing in something like a POD or some sort of Multi-effect board/pedal. You could also just plug instruments straight into an interface and add guitar distortion/effects using some cheap/free software.
www.myspace.com/shattercomplex - project I played with in early high school, years ago, dynamic mic on the guitars, cardioid on the vocals
www.myspace.com/ofwormsandempires - a friends project,most, if not all of them are done with digital effects, newest ones using a boss floor board, all of them are vocal-less.