I'm going to make a different assumption here and assume by "log on," you mean "connect to." Are you trying to make a file server or a domain controller here? If either of these in the case, then previous suggestions that XP Pro will work as well cannot be heeded. Server 2003 is correct here but you're getting into some complicated configuration if you want to do what I think you do.
However, to simplify things, if all you want to do is be able to log into a domain, you'll need to configure your Server 2003 box as a domain controller, create a domain admin account (or make your own a domain admin), and join the rest of your computers to that domain from the Computer Properties window. I'll go into more details if this is the route you want to take but it's pointless to go into all of the fine points if it's not.
As for making it a file server, you also need to add this role to the server machine (which can be done with the "Manage My Server" window that opens every time you start the server. To do this properly, it will also need to be configured as a domain controller with Active Directory so you can set up folder redirection. Again, this is complicated so I won't go into the details unless I'm on the right track here.
To everyone else: A server does not instantly mean a web server so the ISP and its limitations may have no application here.
However, if you are making a web server, you've got quite a bit more to consider though even with ISP limitations, you can run one from your home without issue (I did on Comcast with no problems - you just need a Dynamic DNS service).
As for wireless, as already suggested, it is not suggested for any of the uses I listed. However, if it is the only way to go, make sure both the server is positioned as close as possible to the wireless router/access point. I'd really recommend you run a cable though, even if it's not run properly.
