I felt it was time to indulge myself and buy some hardware - I got a Western-Digital 250GB Elements USB external disk. It comes with no software at all, FAT32 formatted, and is readily recognized by my box.
I decided to format it after checking the disk with fsck.vfat (part of the dosfstools package) - it complained about differences between the FAT's on the disk, and about hidden sectors. The interesting bit of trivia regarding FAT32 is that you can't format a FAT32 volume larger than 32GB - get this - under Windows! Under Linux you just run the following:
mkfs.vfat -F 32 -n volume_name /dev/sda1
(you should, obviously, replace /dev/sda1 with the correct device path). The generated file system (233GB in size) is perfectly usable on both Windows and Linux.
As it happens, I did not specify a volume label, and went on to copy the backup files from the old disk to the new disk. I (and my Linux box) only realized that the volume label was now empty, at the next reboot, two days later. So I needed a way to label the disk without formatting it. This can be done with mlabel (part of the mtools package) like this:
But you must first edit /etc/mtools.conf to make sure that the drive letter c: maps to the correct Linux device path - in my case it was just a matter of un-commenting the following line:
drive c: file="/dev/sda1"
I don't know why this mapping is necessary, but that's how these tools work.
Slack is good.
[7 Feb. 2008] UPDATE: labeling a disk updates just one FAT, causing fsck.vfat to complain about differences between FAT's on the labeled disk - this seems to be perfectly harmless.