HIFM, welcome to Amazing Charts.
You will find many different answers to your question. The best thing is to assimilate from these answers a solution that works for your office.
1st of all, hardwiring is the way to go. You are thinking correctly here. This is always faster than wireless, and you don't have the same issues w/ encryption and security risk that you have w/ wireless. I have taken a hybrid approach. Most of my computers are hard wired but I have two lap tops which are wireless. If you have knowledge of how to secure wireless access points, then it's not a big deal. But if you do not know how to secure your wireless, then don't risk the security.
That being said, it is definitely BEST to have a central server and run your workstations off the server. Therefore your main programs (Amazing Charts and your practice management system) would run on the server and your clients would access their databases. This keeps your system running quickly, reliably.
However if you do not have the resources to buy a server or learn a new operating system (Windows Server 2003 or Windows Small Business Server 2003), then you should have a DEDICATED desktop computer that NO ONE ELSE WILL USE. This will be your peer to peer network.
You don't want a user on the computer that your main databases will be stored upon. It opens the door for system crashes and slows down your network.
In either case you will need another computer. Either a server or another peer to connect to your peer to peer. Keep your 3 other computers in the locations that you intend to use them in.
I hope this helps.