(and they often are) it makes sense to use the ethernet connection. You'll use it initially to configure the router anyway, and you will gain nothing (apart from mobility) if you revert to a wireless adapter. Of course you'll have to do that if you want to move the PC or the router at any stage.
A lot of grief if you run a mixed XP and ME network? There's no reason why that should be the case, but take a tip from me - when you run the home networking wizard on the desktop say 'yes' to the option to have WinXP create a networking floppy disk. It will contain all the necessary configuration settings, and you simply run it on the ME machine.