Gah. Well OK, Staples did not have a WRT54G. Or a WAP54G. Or a WET54G.

They had:
WRT54G-c (compact)
WRT54g-s (speed boost)
WRT54-AG (A+G router)
WGA54G (Game adapter)

I got the Game adapter because its box showed very clearly doing almost exactly the thing I wanted to do: Hook up a standalone device to a wireless network. And it's one that Peter recommended.

Well, I've been messing with the thing for a long time and it keeps ALMOST working, but it doesn't have a built-in DHCP server and I'm having trouble getting it to route the traffic from its input into my LAN. I can get it to connect to the lan and all, I just can't seem to talk to the LAN once it's connected. GAH.