I have no experience with networks but I'm running a school lab with 30+ stations. Most of them run Windows XP Home.
Could I possibly configure all users, permissions and access to course file shares from a new Windows Server?
Normally, you could do exactly what you want, but Windows XP Home is restricted in a way that doesn't allow it to become part of an (Active Directory) domain, which is necessary to manage users centrally.
Access to files via shares on the Win Server will work though, but you need to manually configure users on the client machines.
(BTW, the same is true for Win 7 Home or basic).