The size of the hard disk is not necessarily important.
If the motherboard's BIOS chip uses 48-bit LBA (i.e. a typical post-2001 WinXP system) then any size of hard disk can be installed. It is only if the BIOS uses 28-bit LBA (i.e. a typical pre-2001 motherboard) that the system will be unable to support a hard disk if it's size exceeds 137 GB.
However, in no case can Windows 9x be installed on a partition that exceeds 126 GB. That is the maximum size of partition which a 32-bit FAT can support, because 32-bit addressing (in reality, it is actually 28-bit addressing in key respects) can only provide cluster addresses up to that size of partition, under the restrictions of the FAT32 system.
Windows ME will fall over if the partition size exceeds 126 GB, or the partition address extends beyond the 137 GB barrier, unless special arrangements exist.
Those limitations can be removed in various ways (e.g. installing a PCI Card disk controller using 48-bit LBA, installing R Loew's patches for VFAT.vxd and ESDI_506.pdr, installing the Intel Application Accelerator if the m/board has an Intel chipset, installing OnTrack's Dynamic Disk Overlay boot loader, etc); but without such special precautions it is fatal to install Win9x onto a 160 GB disk.
See this page for further details, and other solutions -