Here's a very quick, overly simplified answer. First, this is really a two-part problem. The first part of the problem is that you want centralized account access; i.e., all computers to have the same logins and passwords (i.e., computers A, B and C all have login "tom", "sally" and "harry", and each have the same password on all three computers). The second part of the problem is that they probably want all of their files available to them, regardless of which computer they login to. (Needless to say, this is a LOT simpler on Unix/Linux (or Mac OS X), but I'll assume that you're doing this on Windows.)
First, if using Windows, people will probably point you to Active Directory for authentication. If you ever want to have non-Windows clients as part of your network, or if you have any interest in doing things a "better" way, avoid this. Try using LDAP for authentication, instead. You seem technically proficient, and learning the "right way" now will help you out down the road. And, it'll save you time & energy (and frustration & licensing fees), too. You may find it worthwhile to have a single Linux box on your network for a "server", that has the LDAP server & main shared file system. But you can also run these services on Windows or Mac.
Second, is the shared files. It's probably simplest if you have just a shared file system that all users can access (using their own login/password), and don't try storing their "home" folder on the share. Windows will crawl if it has to access the Desktop and User directories from the "shared" file system. The file server can run Samba (if Linux), and clients can connect to it using SAMBA/CIFS (a normal Windows "shared folder").