[kosmiq]

FlashFXP is the right app to use. It works great and will do its thing.

To FTP to the xbox you need a standard RJ45 crosslinked cable (standard network cable, crosslinked), or a switch and 2 RJ45 standard cables. I would recommend the crosslink though. Of course you need a network card in your PC that supports atleast 10mbit, 100mbit is prefered though.
Then assign a static IP to your PC and your xbox, connect to the xbox IP usign FlashFXP and copy what you need.

A note about Xbox-Live now that you mentioned it... You will not be able to use Xbox-Live anymore. Erm well you could use it but with the risk of being banned. Especially if you previously has been online with the standard hdd and that number has been regged on xbl. But when chipped you could use a legal and free alternative such as X-Link Kai or Xbox Connect.