Search the forum for "physical computer" and you will find several threads talking about this.
The short answer is that you will need to learn about PGA/FPGA chips. These are chips that you program with a language similar to HDL.
If you wanted to do a "retro" project that used simple ICs, you need to find a source for 7400 series TTL or 4000 series CMOS. If you are in the US, Jameco Electronics is such a source.
These chips do include ALUs (very different from the n2t ALU), but not CPUs.
I have done a design for the Hack Computer,
simulated in Logisim, using TTL chips. This design needs about 80 TTL ICs and 16 2Kx8 static RAM ICs. It does not include Screen or Keyboard. Easiest way to do the I/O would be to use a UART IC for serial I/O.
--Mark