I investigated this somewhat thoroughly before buying my 360 in January and ultimately going with a wired connection. My connection is just as you describe - my internet goes into my wireless gateway which broadcasts the wireless signal for my PC, Wii, and DS, but then I have a LAN cable running from the gateway to my 360 and to my HD-DVD player. If you have an existing wireless network and your gateway/router is close enough to make it feasible to run a wired connection to your 360, it will definitely work.
There are LAN-to-wireless bridges out there, but they're hard to find. It would basically "trick" your 360 into believing it had a LAN connection while it was really connecting to wireless network. Buffalo had one of the better products I found, but they're in some kind of litigation limbo as a company or something.
I have no idea if a generic device like a wireless printer hub or anything would work with the 360 and allow it to connect to your wireless network or not.
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