Knoppix needs about 2.3G to install so it will fit on your 3.2 with a little bit to spare. You can slim it down as soon as it's installed by removing unnecessary stuff (like over 100 meg of extra language support).
You cannot actually install linux on a fat 32 drive but qtparted should be able to add in a linux partition without losing any data.
Is your current HD partitioned or all one big drive? If it's all one partition with lots of irreplaceable data you are courting disaster, I strongly suggest you back up & partition so that the data is separate from the O/S as soon as you can.
If you have a fat32 partition at present, Linux on the old 3.2 drive can use the fat32 data partition so you may not need to have a bigger HD for Linux as it is O/S only.
Knoppix or Kanotix are both good choices for a Linux install, much easier to work with than red hat based systems like Mandrake, SuSe or Fedora & easier to install than Debian.