In lack of a lab power supply with adequate protections, you can try using an ATX psu that has: OCP (over current protection - e.g. short circuits), and you can also read about the acronyms for other types of output protections. But for testing puproses, having OCP is really good, as it "might" help, not sure, but just might.
The arduino uno input has some input voltage rating - read on its webpage. It means its input has a voltage regulator which takes some variable range voltage to create a lower voltage, but stable. Usually does this by dissipating the difference as heat, so do NOT exceed the max voltage for input, otherwise the regulator will get hotter and hotter and at some point it might burn.
Feed V+ and gnd to the stepper driver directly from psu. And feed the step/dir/enable pins from arduino GPIO pins (designated in sketch) directly the the stepper driver step/dir/en. Any driver should work, if you do not want to bother with pinouts of small form factors like A4988 and similar, you can also pay a few extra and use some driver with connectors, like this or something that looks like this. As long as it says its a bipolar stepper driver, it has V+ and gnd inputs, and 4 motor outputs, and it says its driven by logical inputs of EN/STEP/DIRection, then it should work. I am assuming that your sketch requires a bipolar motor driver, coz some of the sketches out there for a single motor might be unipolar which can and might be driven slightly different.
Learn how to wire the motor wires to the stepper driver inputs. Do not disconnect the driver outputs which go to the motor while the driver is energized. Generally speaking about the area of the stepper driver output -> wires going to motor, any mistake in this area will probably cost you one driver. Each time. Otherwise the things should work.
In learning how to make things work together, first thing is to read about each component inputs and outputs. Good luck.
+ About the power supplies you linked, they should work as long as they offer more amperage than all the components consume added together. But you should not simply feed it to arduino and then use arduino outputs to feed the stepper driver, because all the current required by driver will pass trough arduino board, which is not "healthy". Also stepper driver are sort of "switching" consumers and as such they might create transients at its power inputs, with higher voltages than normal wich is also not good for the arduino board. So imho, it is healthier to split the psu output wires and wire both arduino and stepper at same time. This way the current needed by each does not have to pass trough the other one.
The arduino uno input has some input voltage rating - read on its webpage. It means its input has a voltage regulator which takes some variable range voltage to create a lower voltage, but stable. Usually does this by dissipating the difference as heat, so do NOT exceed the max voltage for input, otherwise the regulator will get hotter and hotter and at some point it might burn.
Feed V+ and gnd to the stepper driver directly from psu. And feed the step/dir/enable pins from arduino GPIO pins (designated in sketch) directly the the stepper driver step/dir/en. Any driver should work, if you do not want to bother with pinouts of small form factors like A4988 and similar, you can also pay a few extra and use some driver with connectors, like this or something that looks like this. As long as it says its a bipolar stepper driver, it has V+ and gnd inputs, and 4 motor outputs, and it says its driven by logical inputs of EN/STEP/DIRection, then it should work. I am assuming that your sketch requires a bipolar motor driver, coz some of the sketches out there for a single motor might be unipolar which can and might be driven slightly different.
Learn how to wire the motor wires to the stepper driver inputs. Do not disconnect the driver outputs which go to the motor while the driver is energized. Generally speaking about the area of the stepper driver output -> wires going to motor, any mistake in this area will probably cost you one driver. Each time. Otherwise the things should work.
In learning how to make things work together, first thing is to read about each component inputs and outputs. Good luck.
+ About the power supplies you linked, they should work as long as they offer more amperage than all the components consume added together. But you should not simply feed it to arduino and then use arduino outputs to feed the stepper driver, because all the current required by driver will pass trough arduino board, which is not "healthy". Also stepper driver are sort of "switching" consumers and as such they might create transients at its power inputs, with higher voltages than normal wich is also not good for the arduino board. So imho, it is healthier to split the psu output wires and wire both arduino and stepper at same time. This way the current needed by each does not have to pass trough the other one.