I'm new to the self-employed thing as well (and I'm from abroad so I have a few other things to consider as well). The above mentioned website is very informative.
One thing you might want to consider is the AOPA Instructor Liability Insurance. I spoke to the school where I did my instructor license and they recommended it because there has been a few nasty case's of instructors getting sued by students (I would like to hear the actual details of these cases or if anybody knows where to find material about them) and being self-employed the club will not have any insurance that covers this area.