Connect low-RPM motor to computer PSU
You should use a separate power supply for fiddling around on the bench. Tapping power off of a working computer is adding a lot of unnecessary risk. You can probably harvest a working power supply for free from an old computer. Check the net for how to get it to power up, you may have to put a load on the 5V bus and to short a couple wires to fake the soft power switch. Add a fuse to the 12V connection or you could conceivably burn yourself from a short. Try a 5A inline fuse. You can find easily this as an automotive part. Photos from here and here:





The motor you show, although specs would be nice, I can assure you will operate fine from a PC power supply. It probably draws less than 1A even when stalled. 

You can use the Molex-style connectors that go to some fans and old-style IDE (non-SATA) hard disk drives etc. 



The motor goes between the yellow wire and a black wire. If you reverse the polarity the motor will run in the opposite direction. 

Mostly the motor you choose will depend on the torque and RPM you need. The one you show is 14RPM so it takes a bit more than 4 seconds to rotate through 360°. 

It has a built-in gearbox so it will be difficult or impossible (depending on the type of internal gearing) to turn the output shaft manually without damage. 

The torque rating is usually specified in N-m or oz-in and you will have to evaluate whether it's sufficient if it is called upon to drive with much torque. 

This kind of motor is called a brushed DC motor and simply turns when voltage is applied. It draws more current when you start it and more current as you load the output shaft. 

To get it to turn slower you can lower the voltage with something like PWM or a voltage regulator, however the maximum torque (stall torque) will drop commensurately. More sophisticated speed control methods measure the motor speed (with an encoder or tachometer) or the motor current and raise the voltage to maintain the speed more constant as the torque increases. Some schemes also use back-EMF as a sort of tachometer.