AFAIK, the 360 doesn't have wireless LAN unless you get the wireless adapter for it, same as the original Xbox.
There is no version of XBMC for the 360, because it hasn't been hacked in any practical manner, yet.
For the original Xbox (or the 360, I guess) you'll need an ethernet to wireless bridge or this:
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Both Xboxes are pretty noisy in their stock condition. You might wanna take that into consideration when planning on using them as a media player.
I'm using an original Xbox, that I modified. The cooling fan has been replaced with a quieter one and the harddisk with a quieter model with more storage capacity.
You'll want the remote kit to be able to use an infrared remote.
I'd also recommend an IR-Hack to be able to remotely switch the Xbox on and off, a feature that the remote kit doesn't offer but comes in very handy if your box hangs. Its just so much more elegant and convenient than having to get up and press the power button.
The 360 offers video playback through UPnP, I don't know if it supports DLNA but i suspect so. It is a bit choosey about the AVI files it wants to play back. I have one and I tried with TVersity. With a good UPnP server and a decently powerful computer on which said server is running, you should be able to transcode on the fly, which should make the 360 more flexible. There have been many articles on xbox-scene.com about that. I haven't tried any, so it's up to you, if you want to take that road.
HTH, uwer