This is a huge topic. I just completed a selection process at the college where I'm IT Director for a system such as you describe, and I can tell you that they run into the hundred's of thousands of dollars or more, depending on school size. This is especially true when you tack on that billing requirement (most SIS-only systems don't do much for billing). The list of potential vendors is lengthy:
I pulled this list from several options that our college looked at. This is just the tip of the iceberg. I can tell you that we selected Jenzabar EX/JICS. We're just beginning the implementation so I haven't formed much more of an opinion of the software yet beyond what was demoed for us, and it's targeted at higher ed anyway (as are several others listed here). You'll have to go out there and do a lot of research to find out what option best fits your needs, and that's just the beginning. You'll also need to create buy-in from faculty, staff, and administration, and implementing these systems isn't usually very turn-key either.
I can also say that you don't want to roll your own. There are two reasons for this. One is the "hit by a bus scenario". Imagine you build this and are the de facto only person who has any hope of supporting it. Then you get hit by a bus or for some other reason are not able to work on the system. That really leaves the school out cold. The other reason is government reporting requirements. A huge benefit in choosing a product with paid maintenance is that you know they're keeping up with all the changes in the required reports every year, and even if for some reason they don't, there will be enough other schools with the same vendor that you have combined leverage with the government to avoid penalty.