Here's my understanding:
If you want people to be able to connect/manipulate/use your database (DB) from anywhere (such as the internet), then you need FM Unlimited. It's a webserver that specifically works with FM databases. All you need is a browser (IE/Netscape/Opera) to access the DB. One caveat: the users won't be able to do everything (READ: most things) that they would be able to do from FileMaker Pro (FMP). It works with the Internet and intranets.
If you need more functionality for your clients (users) then you'll need FM Server to serve up the tasty DB's and FMP clients to access the DB's. Every single computer that will access/manipulate the FM DB's will need a copy of FMP loaded on it. A site license or VBA package will probably save you money.
What you described is using two seperate machines, one with FM Server 5.5 on one and FM 6 Unlimited on the other, with the Unlimited machine pulling the DB's from the Server machine. My question is this: Do people need to connect to the DB's with FileMaker Pro clients, or would it be better to save money and eliminate the Server machine and the FM Server 5.5 software? If you need people to be able to connect via their web browsers AND FMP, then you DO need both.
Otherwise, you could just load Unlimited on your dedicated web server machine, develop the DB's on a machine with FMP loaded on it, and store the DB's on the FM Unlimited machine for access from the 'net (doing all of this via TCP/IP). I hope you understand... my explaination got a little convoluted because I tried to make it decipherable for a newbie. Just looking out for your bottom dollar...
Cheers,
-Ansel