The target is to be able to build Linux 0.12 using modern gcc and run it in QEMU, or preferable on a true 80386 machine. AFAIK, modern gcc still supports this architecture, so in concept this should be possible. There might be a LOT of changes in source code to be made, though.
The idea behind is to obtain a very old Linux that can be built easily on modern systems, with modern C support, and gradually add my own stuffs using the same tools, so that I don't limit myself to very old toolchains.
Edit: The reason to pick Linux 0.12/0.92 is because 1) It is kinda complete (without network I believe) but not too complex (I believe the loc is under 20K), and 2) It is not a toy OS and can run on real hardware (a 80386 machine), and 3) we have an excellent book for it: https://download.oldlinux.org/CLK-5.0-WithCover.pdf