Not quite a simple question to answer for a few reasons so I'll give you a few views from a few different angles from my experiences.......
As for the cards themselves, most of those machines would be best - speed-wise - using a 10/100 PCI Ethernet Card. ALL ISA Ethernet cards are 10mbps. The reason why is limitations in bus-speed imposed by how fast these particular busses run. ISA I think is 4.77MHz....maybe 6MHz in some systems, but a PCI slot is usually 33MHz (maybe it's 66MHz). So that's the speed side of the picture.
HIstorically, most, if not all Windows For Workgroups 3.11 systems had ISA Network cards, so once you get to cards from about 1998 onward, support for Windows For Workgroups 3.11 starts to dwindle off on anything that's PCI 10/100. The reason was when WFW was the thing to have for a networked PC, the Intel 80486 was king, and most 486 systems, at the most capable until about mid-late 1994, were VESA Local Bus or EISA at best, and many only had 8/16 ISA slots like the 286 and 386 machines before them. As such, by the time of Super Socket 7, a lot of card makers stopped offering NDIS2 and NDIS3 drivers for Windows for Workgroups - instead focusing on drivers structured for Win 9x and NT.
DOS, however, had a different path. DOS was still being used for some specialized applications in business, so they continued support for packet drivers and even NDIS and ODI drivers for DOS until sometime toward the middle of the first decade of the 21st century. I was still finding tutorials for setting up a Networked DOS boot floppy for some NT-related purpose as late as 2008. Most people today set these ups with Mike Brutman's mTCP Suite using a Packet Driver. However, the networking was not that far off from Windows For Workgroups in that the DOS portion of WFW was basically the main parts of Microsoft Network Client and/or Microsoft LAN Manager for DOS - which was how you got a network going on the Microsoft side prior to Windows for Workgroups.
If it were me, I'd probably see what busses you have in which computers . The first three I'm more than sure have PCI, if you can find an older 10/100mbps LAN card in PCI, you might be able to find a DOS packet Driver and the NDIS2/3 drivers needed for WFW to make it work. The AMDx5 I'm assuming is one of those AMD 5x86 PR75 133MHz Socket 3 machines that's basically a 486 by platform, so that - in lieu of PCI slots, you'd want to go ISA with that one, and that would be the best one for WFW and DOS networking because it'd be the easiest to support.
To answer the question regarding support with DOS games, I think it depends on the game, TBH, I've never used networked DOS games yet except using DOOM95 and that's basically Windows Gaming. Most DOS games I've seen used IPX/SPX protocol. I can't think that it would not work with a PCI card assuming it's a chipset that supports DOS. That's the biggest part is the chipset being used because some cards came in PCI AND ISA, and I recall even seeing some cards (real oddballs) with a switchable backplate and both Busses supported - though they're kind arare. Intel, RealTek (ie like the RTL-8019), LinkSys, and NetGear seem to be the best bet when it comes to compatible cards for most legacy DOS/WFW stuff. SMC is also a really good one and it seems they kept support a really long time.
