I forgot about the wireless connector. That is a long way to go and a few levels to go through. I think it depends on how good your connection is. When we first bought a good computer, our router and modem were in the great room, pc in the kitchen. Straight shot, no obstructions. We dropped signal all of the time.
The antenna will cost between $75-100. I guess there are two different kinds now. One for wireless N. We're heard that you can use a generic wireless antenna but have never tested it, nor have any of their friends. Best speeds still seem to be with the ethernet cord.
Our set up now, we do have the wireless but the xbox is in the same room as the modem & router (office). It doesn't have to go far, no obstructions. They can move this into the family room or basement without an issue but it's not that far, not many obstructions. The wireless antenna will only work as good as your router will let it (speed) and the limited obstructions.
Do you have a laptop to check and see if it will work well that way?
If not, you might be able to run an ethernet port to the room. My brother in law did this for us, for our boys to be able to use the internet more easily. It took an afternoon. We did not want to have a bunch of wireless cards after the first and only experience we had with it.
Also, with xbox live, they get to talk to each other. Anyone and everyone. Ours is in the office because on the few occasions that I haven't been around and walked in, there have been some foul mouthed and rude people on there.
I believe you can buy this and put it up. It is not activated until you key in the code. Same as when you buy it at a b&m store.