Multiple user VCN client?

Hey everyone. So, there is a Mac computer set up at my school for our radio station, and I'm wondering how difficult it is to find a remote desktop program/service that can allow more than one person to access the same computer. Not at the same time, of course. But, in other words to have like...multiple accounts set up on the program so that people log in to the remote access system with a password and it knows who is accessing the computer, and then move about their business. I'm not sure if this makes any sense, but that's what I'm wondering. If you need clarification, I will try my best to provide it. To let you know, I'm looking for something in the range of free - an inexpensive one-time purchase (I would prefer to avoid a monthly subscription cost). Thanks all

Do you know what version of OS X is running, and do you really mean VNC - Virtual Network Computing

What version of OSX radically effects what solution is easiest

It has Mac OS X 10.5

I was under the impression that "VNC" and "Remote Desktop Client" amount to primarily the same thing, but please correct me if I'm wrong

OK then, its built into Leopard but called screen sharing

The people connecting to the machine will need to run a VNC client like Chicken of the VNC for Mac or TightVNC for windows

Heres how

Remote Control Leopard with TightVNC

this article seems to assume that the vnc users will be on the same network as the computer that is being controlled. does this have to be the case?