theres no real reason to keep stating what iv already said OC, but what your forgetting is this is a school network and at some point its going to at least need some form of managed DNS/Cache/Web filters
so while the
"16 PC's" <=[-]=> "Switch" <===> [wireless]"Router"<===>"Cable Modem" is fine for home use.
it's going to eventually need at least this.
"16 PC's"<=[-]=> "Switch"<===> [wireless]"Router" <===>
"D/C/W/Filter" <===> "Cable Modem"
once the OP has got this back up and running in a better long term managable way (make that LAN plan drawing ASAP etc) he might also think about putting in a few "FreeNAS" (wireless)LAN storage devices to put any old kit back into service, you could even make a few IT lessons out of it to give everyone some realworld experiance, its fun too
<=[-]=> = wired or wireless connected PCs to switch or wireless router