I would recommend developing an operating system for the classic Amiga computers, which had different versions of the 68000 processor. Since the Amiga computer is a complete computer and is extremely well documented, I thought this would be a good exercise.
There is an emulator for it called UAE (and Win-UAE) which is very exact and
can be configured with different kinds of processors (68000 - 68060) and other capabilities. Normally, you would also need to acquire the copyrighted ROMS to it, but since you are developing an operating system yourselves, this is not necessary.
Tools you will need is either Cygwin (for developing under Windows) or a Linux computer. Then you will need cross compilers. This includes both a C compiler and an assembler. A template for creating a simple ROM which changes screen color and flicks the power LED can be found at the hyperlink below. It will create a file 'kick.rom' which UAE then searches for in the current directory.
Reference on the 68000 instruction set can be found at the link below. Be aware that different assembler programs may use slightly different syntax and instruction set.
If you need to demo the operating system on real hardware, actual Amigas are still extremely cheap and abundant on Ebay.
I would post links too, but stackoverflow will not let me, I have too low reputation so here are the references with links.