How are Circuitboards with Multiple CMOS Chips Routed?
The classic layout technique with double-sided boards that mostly contain DIP packages is to run traces (primarily) vertically on one side and primarily horizontally on the other. Power is routed first to keep the traces low inductance, and bypass capacitors are placed at every chip, usually. Typically the power pins are at the corners. 

That technique is pretty useless in the current year because SMT packages often have leads on each side, and the level of integration is much higher. 

If you're using perf board you should take care of the power and bypassing first and then run the signal lines. Your proposed layout looks fine to me. I've done many prototype perf board setups using polyester solder-through magnet wire (in the distant past, now it's easier and better to lay out a PCB and have it manufactured). Here's the back of an LED display board for an instrument prototype: