It depends how you want to use the WIFI
I recommend you physically locate the file server near the wireless router, and then connect the file server using an Ethernet cable to the router. All other wireless computers on the network will be able to access the server, but the server does not have to be wireless compatible. Doing this removes the need for the server to work with wireless cards, which is a sticking point for Linux.
But Linux thrives on Ethernet cables and this would allow you to use your old machine and Linux to make a file server, which is what I do.
My setup uses an old Gateway with 500Mb of RAM, a 640MHz Athalon processor, a SATA PCI card and 2 150 GB drives configured as RAID 1 (Mirrored)
I run OpenSuse 10.2 and SAMBA to service a Windows network. The system stores files, streams video and music and is my print server as well. The network services wired as well as wireless machines over a wireless router.
You specified Windows Vista, so make sure you are using the latest version of SAMBA, which supports Vista networking. (not the same as XP networking. (Gee, was Der Bill trying to make life hard on the open source world? Hmmmmm)
Anyway, that would be the best solution I can think of. Your only other solution would be using XP and trying to make it act as a server using shared drives. It might do the job you want, but would be slow on a 1Ghz machine unless you have a lot of RAM and the shares will be open to all. You will not be able to configure private shares or implement good network security.
I have not tried this and do not know how well XP would handle multiple file access requests. You'll have to load patches from MS to make it work on a Vista Network
Server 2003 would be a heavy load on that machine and I am not sure about WIFI and Vista compatibility, as well as cost and availability.
Server 2008 is a non starter - your hardware will not support it.
E-mail me if I can help with the project