Installing DOS
So, do you have some DOS installation disks lying around from back then and a physical drive in your pc to read them? If not, you got a bit of a problem: You can download images of the disks from many places on the Internet (like WinWorld), but how do you write them to diskettes - or your GoTek drive? As far as I know of, you can't write them to USB diskette drives (apparantly writing images require controlling the drive in a way USB does not support), and you can't do it on your "new" old pc, without having an operating system on there - it's pretty catch-22.
If you have a Gotek, it's pretty easy. If it is a stock Gotek, you can use ipcas software to wite the images to the Gotek USB and boot from that - see the Floppy page for link and how-to. If you have a Gotek with FlashFloppy, even easier - just copy the disk image files to the USB and boot from the first one.
If you don't have any of these, it gets a bit more complicated. Renaud Bédard has a guide on theinstructionlimit.com on a way to do it. If does require you have a way to connect your Compact Flash card or IDE hard drive to your modern Windows machine. Yes, it's a bit complicated, but I can't really think of any other way to do it...