Wallet ID, where do I get one and how does this stay unique to me?
They are called private keys, which correspond to public keys, or bitcoin address. There is no guarantee that it will belongs only to you, but the chance of generating the same key is so rare that it might as well be unique to you.
BitcoinGUI, do I need to have another program installed that this runs on top of?
Bitcoin is a sufficient tool for conducting economic transactions.
How do I transfer funds? Do I need a central server account? Does the wallet ID suffice?
Transfer is done through "send bitcoin". You will need the owner's bitcoin address for you to transfer bitcoin. Likewise, you will need to provide your bitcoin address to the person who needs it to send bitcoin to. There is no central server as bitcoin is completely peer to peer.
I hate to be the new guy asking dumb questions, but I can't find any clear answers to these questions.
The fact that you done your homework but still have questions mean that the FAQ is inadequate or incomplete.