HyperBBS is written in HyperCard. Therefore, you need a Macintosh to run it. Furthermore, you need a Mac that can run HyperCard. If you can read this stack on the machine, you can run HyperBBS on it.
BBSs use disk space. A message oriented BBS will use a moderate amount of space. A file oriented BBS with an active user population will use as much disk space as you can afford. Also, the more space available, the less of your time needed to prune it.
Two 800K floppies is the minimum needed for HyperBBS. A 20MB hard disk is best.