Ok, the thing you sit at is typically a dumb terminal. It does almost nothing. The server is called a server.
Anyhow, 10mbit should work for those, but 100mbit makes it a lot smoother. I got the chance to use one briefly at a SUN training center and I was half inspired to sell my family to buy a setup.
These thin clients are nifty. I think the one I used was closest to the 1g. Anyhow, everything is run on the server, and I think you can have just about any sun server for this, but there are minimum requirements depending on how many clients.
These thin clients let you have a smart card keyed to you. You enter your username and a password after putting the card in. Your desktop pops up. If your workstation is being used by someone else for some reason, you can jump on another one, pop in your card, login, and the stuff you were working on before lunch comes up. Everything is stored on the server (have I mentioned that yet).
You need a fairly beefy server if you have a lot of clients. Can't remember the specs, but they should be in the documentation there somewhere. With OpenOffice/Staroffice, I'm thinking that these could be a great solution for offices.
Hopefully that rambling gives you a place to start.