The problems I can see with your plan are the following:
1. A HDD of 1GB is probably not enough to store a lot of MP3s.
2. 32 MB of RAM is probably not enough to run a lot of window managers. Not to mention play MP3s at the same time.
Launch the installation of Slackware, choose the "expert" option, and leave out everything, *except*:
"A" packages (base system).
"N" packages (networking -- make sure you have Samba)
"X" packages (X11R6)
Then, install "xmms" (should be in the "G" packages or in the "XAP" packages).
Then, install a very light windows manager. I think Fluxbox is your best bet here.
Configure everything and make sure it works [yes, this is the hard part!]...
Create an SMB share on your windows machine and make sure your laptop mounts it.
That's it! Your laptop should be able to play MP3s from your windows machine. Another solution would be to install another Slackware PC as the MP3s server, mounting the MP3 directory with an NFS share instead of SMB.
Hope this helps...