ZDoom

Not really sure, actually it can run even without SSE but the releases require it (you'd need to compile it yourself without the SSE2 option and provide sound dlls not requiring it). I tested vanilla on a P3 and it was playable. You don't need D3D either as it runs with DDRAW. Just try the rogue devbuild at gzdoom-vintage.
In theory it should run on 98 but you'd need to create your custom cross compiler for MinGW-w64 (i don't know how to do it not that i'm really interested and the same for the dlls). Recently i made the switch to the Unicode API but i don't think that would be a showstopper as KernelEX would use the Unicode extensions if they're available, in theory.
So yes XP required becouse of the compiler.
So it should run on your toaster (guess you want to play some lan games?). Also ZDoom32 will run much better on that hardware and ZDoom LE even more and on GL 1.x.
If there was some interest may be i could add complete decorate support to ZDoom32 updating the VM but seems that's not the case.

As far as I know LZDoom requirements are much more lax. Any processor that supports SSE is sufficient, along with any semblance of a GPU from 2003 or later (as long as it supports D3D9). I think you can use older versions of Windows with it, too, but not entirely sure.

Just keep in mind that if you plan to run hardware mode with LZDoom, an OpenGL 2.1 card or later will be required.

Oof. Sticking with PRBoom on the old EeePC 900 then.

I wonder what the numbers are for LZDoom though...

I am not sure, to be honest, but this is what I would recommend:

• Quad core 2.4GHz 64-bit processor with an updated 64-bit operating system
• A dedicated GPU from 2012 or later, or integrated from 2016 or later (One that supports Vulkan would be recommended)
• At least 6 GB of RAM

The bare minimum to run it at all with a shitty framerate would probably be this:

• A processor that supports SSE, with Windows Vista or later
• Any GPU that can support OpenGL 3.3 or later
• At least 2 GB of RAM

What are generally considered the minimum target computer specs to run GZDoom smoothly and reliably?

Let's assume all default settings, we want minimum 35 fps, <10 seconds startup.