What is the simplest instruction set that has a C++/C compiler to write an emulator for?

Easiest would be to invent my own instruction set

uh, ok, we might come from very different experiences here…

With easiest I mean the least amount of instructions.

That's not necessarily the easiest to implement. Often, having more instructions is a good complexity tradeoff compared to having more complex instructions.

So my question is, what is the easiest instruction set/architecture that has a (hopefully stable) C++ and/or C compiler?

This sounds like no job for C++, so let's concentrate on C. (If you don't understand the difference having C++ RAII paradigm makes, you might not be in the optimum position to design your own ISA.)

Puh, some microcontroller instruction set that is early, but not too early (because too early would imply "designed around the limitations of digital logic of that time, like e.g. 8051).

AVR might be a good choice, though I personally don't like that too much.

I hear Zilog Z80 is easy to implement (there's really several Z80 implementations out there), but it's pretty ancient, and not very comfortable (being from the mid-70s).

If you really just want a small core to control what your system is doing, why not pick one of the many processor core designs that are out there?

For example, RISC-V is a (fairly complex) instruction set architecture, with mature compilers, and many open source implementations. For a minimal FPGA core, picoRV32 would probably the core of choice. And on a computer, you'd just run QEMU.

You should take al look at the PIC microcontroller family. The instruction set is limited to 35 different instructions, while the controller is actually still used. Look at the datasheet at page 228: PIC16F datasheet

The controller is using 8 bits and is also available with less periphery, but that does not change anything for the instruction set.

You need a One Instruction Set Computer (OISC)

A one instruction set computer (OISC), sometimes called an ultimate reduced instruction set computer (URISC), is an abstract machine that uses only one instruction – obviating the need for a machine language opcode. With a judicious choice for the single instruction and given infinite resources, an OISC is capable of being a universal computer in the same manner as traditional computers that have multiple instructions. OISCs have been recommended as aids in teaching computer architecture and have been used as computational models in structural computing research.

Whether a compiler exists, I do not know. But I suspect some unlucky student somewhere has probably been assigned the task of writing one.