To answer your question. A full installation of Windows 98 or later on a 128 MB hard disk can be very difficult, if not nearly impossible without having to go through hacks and workarounds.
Per the system requirements, upgrading from Windows 3.1 or Windows 95 will reuqire at least 120 to 295 MB of disk space (195 MB typically). For a new installation on a FAT16 partition, you will need 165 to 355 MB of disk space (225 MB) and for a new installation on a FAT32 partition, you will need 140-255 MB of disk space (typically 175 MB).
You will need at least 16 MB of RAM for the original version and 24 MB of RAM to install Windows 98 Second Edition.
Windows Millennium Edition requirements are much higher than that of Windows 98.
Also, 98lite, 2000lite and XPlite are all not free: https://www.litepc.com/download.html
When I first installed Windows NT 4.0 on a 7.84 GB SCSI partition on VMware, I couldn't use the whole partition from the get go. The original release of Windows NT 4.0 doesn't support hard disks larger than 4 GB on install and larger than 504 MB on a SCSI hard disk image.
Prior to installing Service Pack 6a, I had to reduce the size of the swap file to fit below the 500 MB limit before applying the service pack. I used Partition Magic to resize the hard disk to its maximum capacity after applying Service Pack 6a.
If you want to install an operating system on a 128 MB partition, you would be better off using Windows 95 (either the original release or OSR1) or OS/2 Warp 3 (Red Spine or Blue Spine version).
For best results, I would prefer MS-DOS and either Windows 3.0 or Windows 3.1 or OS/2 2.x as these OSes use a lot less disk space.