I use XP Pro 32 bit as a daily driver (gaming mostly) and I optimized it somewhat to get 167MB used at boot. On a normal system with less optimization would be ~180MB used. After a few days of use it sits around 250MB, largely due to caching.
My Debian stable (Jessie) 32bit file server only uses around 55MB idle (no x, just ftp). My desktop machine before it died ran Devuan testing 32 bit which used around 80MB at boot without X running. I only used icewm on it though. I could get it lower by compiling my own kernel, but not really worth the hassle.
The main problem with Linux nowadays is when you install large DE's like KDE/Gnome/whatever you end up with a bunch of unnecessary desktop related services installed even with X stopped. 64bit should add some memory usage, but not the large numbers I am seeing.
Unfortunately my FreeDOS rig is down at the moment otherwise I would get you memory figures from it. Memory usage with networking would be troublesome though due to pretty much every packet driver using different amounts of memory depending on how good the NIC vendor is about optimization. I have seen some packet drivers using less than 20K, but others nearly 80K, and thats just the hardware I have laying around. As for running a GUI on such a system, OpenGem would be what I would test with (pic related), but Arachne while ultimately just a web browser lets you do many filesystem functions with it.
I had Win2000 for years but I cannot recall the memory usage from it offhand. I just remember I was able to get it to run on a machine with 32MB of ram without drastic performance issues at one point. I think the numbers were comparable to my stripped down XP install though.
At least for a start, it would probably be helpful to know the minimum requirements of 95/98/ME until someone comes up with hard figures.
95: 386DX with 4MB (8MB recommended) ram
98: 486DX/66Mhz (Pentium recommended), 16MB ram (24 recommended)
ME: Pentium 150Mhz (Pentium II 350Mhz recommended), 32MB ram (64MB recommended)
From personal experience, 95 and 98 benefited greatly from 512MB of ram if you had it. 98 (not sure about 95 but i'd assume so) needs a patch to see more than 1GB. WinME on the other hand really needed 1GB+ before it was happy, otherwise you could expect frequent bsod's.