Instead of trying to wire up dozens upon dozens of NAND gates (which will be by far the most common logic gate in the full design) I routed a small PCB that fits 8 copies of 3-input NAND gates connected to a 4 pin pinheader each. On the PCB there are also common power in & power out connectors .

The PCB is only 20x160 mm (about 3/4 x 6 inch) so they're rather cheap to have made so I ordered 100 pcs of them from Dirtypcbs.

I also ordered a few thousands of transistors and diodes from a local company - I'm sure the parts will arrive long before the PCBs, so I have to start with using my old breadboards :-)