PC power source question

Hey there. I am building a CNC, pretty much from scratch. The "driver" for 3 steppers I made consists of 3 L293D H-bridges and 2 74HC595 shift registers. Purpose of the shift registers is just so that I don't have to use 12 wires going from the Arduino. I modded an old PC power supply, I just cut off the wires, put some connectors there for easy access and attached 2 bulbs for dummy load. I am now wondering-is it safe to just connect all the grounds and provide 12V to the motors across the bridges? Also, it might be more convenient to use the 5V power source output for logic, but it's recommended to use 7-12V to power Duino. And 12V seems to be the upper limit when things are getting inefficient. So... what should I do? if I connect +5V from Arduino to all the logic chips and +12V to the VSS of the L293Ds and connect the power supply ground to the Arduino ground, am I good to go? Also, will I need decoupling? And if so, 100uF capacitor in parallel with each chip should be enough, right?

Firstly test one controller + motor at a time with the power supply, with Arduino powered from USB at first - fewer things to go wrong.

Adding 2k2 resistors in line in the logic signals from Arduino to L293D's will afford some protection to the Arduino and is a good idea when
first assembling things.

You can use a 9V or 10V regulator chip to drop the 12V down a bit before the Arduino power-jack - this affords some protection from drop-outs on the 12V power if the motors are pushing it hard.

What motors BTW? Have you ensured everything can take the maximum current drawn from all the motors?

MarkT:
Firstly test one controller + motor at a time with the power supply, with Arduino powered from USB at first - fewer things to go wrong.

Adding 2k2 resistors in line in the logic signals from Arduino to L293D's will afford some protection to the Arduino and is a good idea when
first assembling things.

You can use a 9V or 10V regulator chip to drop the 12V down a bit before the Arduino power-jack - this affords some protection from drop-outs on the 12V power if the motors are pushing it hard.

What motors BTW? Have you ensured everything can take the maximum current drawn from all the motors?

I made my mind-now I take the logic power from usb. I also used decoupling.
The current L293D chips are designed for is 600ma. I provide 12V at 24ohms-500ma. So I should be safe.
I have the L293Ds in sockets for easy replacement-is this a good idea? I mean, will the heat sink be effecient when it consist just of blob of metal on ground pins of the socket? The chips have heat protection, but still... Thanks for your reply, I really appreciate it.
(By the way-I have tested my setup with one motor so far. And it seems to run fine, I am just a bit concerned about the heat dissipation.)

The L293 will always run hot as it has darlington outputs - proper heatsink a good idea, and if small then a fan to cool it is a
possible fix. I would always recommend a suitable MOSFET driver for lower voltage (< 24V) motor control as you can then the whole
supply voltage across your motor! The problem is that most MOSFET motor drivers are surface mount chips which aren't breadboardable.