Start with breadboards. If you are interested in approaching it from an algorithmic level, the easiest route would be to use 7400 series logic and start with the very basic stuff first: how to make an adder using switches as the input and LEDs as the output; then step it up to use shift registers as rudimentary memory to store the input and output; then figure out how to decode the output shift register to display the result in hex on 7-segment displays. Along the way you will learn about things like Karnaugh Maps and timing circuits.
Beyond that is outside of my experience, but building CPUs seems to be a bit of a hobby these days. I have found Ben Eater's videos to be enlightening. I think he built a CPU at one point, but even the tutorials using a 6502 are useful since he reasons through the construction of supporting circuitry. I haven't watched much of James Sharman's work, but he is building a CPU and carrying it through to the PCB stage. The videos I've watched (related to producing video signals) included reasoning through the design process.
EDIT: I'm not suggesting the microcontroller route since it sounds like you want to explore how to build a CPU. A microcontroller is a CPU with integrated memories and peripherals, which is too high level. (Granted, if you aren't interested in a particular aspect of CPU design you can use a microcontroller to fudge it.)
Beyond that is outside of my experience, but building CPUs seems to be a bit of a hobby these days. I have found Ben Eater's videos to be enlightening. I think he built a CPU at one point, but even the tutorials using a 6502 are useful since he reasons through the construction of supporting circuitry. I haven't watched much of James Sharman's work, but he is building a CPU and carrying it through to the PCB stage. The videos I've watched (related to producing video signals) included reasoning through the design process.
EDIT: I'm not suggesting the microcontroller route since it sounds like you want to explore how to build a CPU. A microcontroller is a CPU with integrated memories and peripherals, which is too high level. (Granted, if you aren't interested in a particular aspect of CPU design you can use a microcontroller to fudge it.)