I have been gaming wireless with my 360 for a few years now - I've always found the signal strength from the wireless adapter to be nothing but good to excellent - even in my old shared house when the router was a bog standard model on the ground floor and I was in the attic room!
For me the only thing that affected signal strength was other people using the internet at the same time, and less so the distance my 360 was from the router.
I think the truth of the matter is though you'll only really find out how good or bad it is until you try. If the signal strength isn't all that great there are solutions - homeplugs, for example. Wireless is the obvious answer for you from the sounds of it - you just have to legislate how many walls the connection has to travel through, and how many other people might also be online regularly - as I say above.
BTW in terms of alternative methods, a router with a stronger signal would undoubtedly help if you're having issues but I'd advise only taking that into account if you find your current router doesn't do an adequate job.