Make the staff members of a group and students members of a different group. Then you decide what rights each group has. By default, the Everyone group has access to all shares.
Since you have a single server, then it has to be a DNS server in order to also be an Active Directory server.
You normally use DHCP simply because, by default, all PCs are configured to automatically receive an IP address. The same with servers, but you obviously need to change that to a staic IP address. Using DHCP means that PCs only have to join the domain (a task performed by a domain administrator), but you don't have to document and assign an IP address to each PC.