Help on setting up a different home network

I'm going to set upp a wireless network at home with 3 computers. My dilemma
is that i use different OS on those and one of them is an pretty old thing
in my basement that i'm using for interfacing with electronics. For that
reason i have decided NOT to use wireless PCI cards wich more often than not
only is supported with a few OS and demands faster computers wich the
basement computer isn't.

My first thought was to use Ethernet to Lan adapters like the d-link DLW 810
or DWL G810 with the ethernet cards on my computers. They are supposed to be
invincible for the computer and requires no drivers. I have drivers for
almost every OS there is with the ethernet cards.

But why make it simple? I found out that D-links AP DWL 2000AP+ is cheaper
and has four different modes wich would be an advantage if i'm going to make
any changes later on. My problem is that i dont know s-t about networkning
and even less about wireless networks. I found out it should be possible to
use four DWL 2000AP+ and a router with the first one to set up as a AP and
the other 3 setup to AP Clients. Now to the big question>

Is it possible to set upp an wireless networks like this?

http://w1.586.telia.com/~u58613751/network.jpg

Regards Mikael