I would contact your school's ITS department and see if they have space on the server for organizations. That would be the best way to go, and I've heard that some organizations even specify that you host it on their server or your school's server. You could also ask your inter/national HQ if they have space for chapter sites as well. The easiest and best route is through your school, though. Our chapter used a FTP program called Filezilla to upload it to the chapter's folder on the ITS server and that was really simple and easy to use. If all else fails and you need a FTP program to work on your school's server, shoot me a PM and I'll send you a copy of it.
Other than that, I've been using
www.brinkster.com since high school for my personal site (which needs updating badly, but that's a whole 'nother banana). They've put ads on their site now, but it's only a banner ad at the top and it's not too expensive to get hosting without the banners.