I'm not sure what you mean by "minimal set of instructions". What is more important for bootstrapping is to restrict the programming style used to write the compiler. So if that was the goal I would implement pointers and maybe arrays, and not implement other types such as structs (which can be useful but add complexity to the compiler, i.e. it is no longer the case that a value fits in a machine word). Functions and function call would obviously be useful to add. But that's about it.

What I'd love to do someday is to write a compiler for a fairly complete C subset in POSIX shell. The goal would be to use only a POSIX shell and this compiler to compile TCC, and then use TCC to bootstrap gcc, all from source. This would be a great tool for reproducible builds from source. If someone here finds this interesting and would like to help out, please reach out to me.