Should be able to pick one of those up on ebay for like $20 if you wanted. (a 166-MHz is going to need a PATA drive, not a SATA one).
You also need to watch for the HD size limits, back then if you had over a certain size, you needed a special translation bootsector to make the rest of the drive available. (I forget the sizes, there were several of those limits that had to be patched). One of them was 137GB, .. wait, here:http://www.tldp.org/HOWTO/Large-Disk-HOWTO-4.html
Limits were 528MB, 2.1GB, 3.2GB, 4.2GB, 7.9GB, 8.4GB, 8.5GB, 33.8GB, 137GB, and 2TB All for various reasons and affecting various technologies involved (e.g., BIOS, filesystems, bootloaders, what-have-you).
You're probably looking at the 33.8 GB limit with a P-1 166 Possibly even the 7.9 or 8.4 GB limit. There is software to get around that though, like I said. MaxBlast for Maxtor and EZ-Drive for Western Digital. You sometimes had to set a jumper in the back of the HD to limit what the BIOS saw, and then use the MaxBlast or whatever to reenable it on boot. (MaxBlast would chainload the normal bootloader afterwards.)
/blast from the past
tl;dr Make sure you ge and IDE drive and that it is relatively small. I would think 20GB would do, or perhaps shoot for 6GB, depending on your cpomputer. You could also see if you can get a BIOS update (ha! back then they were rather rare, most BIOSes could not be re-written without a UV light if at all). Might be better off getting a Maxtor or Western Digital just to be sure you can use the software workaround if necessary.