Ben Eater's breadboard CPU is a good way to learn the basics, but since the focus is pedagogical, it's very underpowered for the quantity of chips it uses (and you better enjoy forming wires). For a much more powerful computer built around the same number of TTL chips, see the Gigatron.
And no microprocessor!
But as I understand it the kits are no longer available :-(
Sadly, Marcel van Kervinck (one of the two creators of the Gigatron) passed away in 2020. You can still buy PCBs on Tindie, and the parts are easy to procure, it's all standard 74HCT chips. You can find a detailed bill of materials on gigatron.io, and the PCB files are there as well.
The one unavailable part is the fancy wooden box.
RE .... See the Gigatron. Google link https://www.google.com/search?q=Gigatron+CPU&oq=Gigatron+CPU gives lots of good explanatory links . (I had never heard of it , it looks quite interesting .... )