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Basic DC Motor Questions for a simple project

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Hello r/robotics! I have a small project kicking around that I need some help with. While I am not new to the field of hobby electronics, I have never used DC motors before and need some help. Either by pointing me to some educational videos or otherwise, I'll take what I can get! (If this isn't the place to ask, please direct me to a place I can ask! I asked a question like this in DIYElectronics but the responses left me more confused.) SO I have a setup like so. I want it so that when I press a button, both motors go to a set position. I want several button inputs, each coordinating to a different position on the DC motors. The weights would never need to spin constantly, just go to a position and stay there until a button press tells it to go somewhere else. Not picky on speed, but ideally want 14RPM under load but can go down to 3 RPM under load. I know enough that I will most likely need a mircocontroller of some sort (planning on using an Arduino) but how would I relay the motors position back to the microcontroler? I've read about something called an encoder, is that what I would need? Can any encoder work with any DC motor? I had my eye on this DC motor would that do what I need it to? DIYElectronics recommended servo or stepper motors, but in order to get the torque I need, these become a pretty pricey option, but I am open to anything that would get the job done! Advice? Tips? Knowledge? Thanks in advance for your time!

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For position control with a dc motor you need an encoder. Best is to buy an encoder with a motor. These are usually fixed to the back of the motor on the drive shaft. So you need a specific motor encoder  combination.

 

For your project a stepper with a stepper motor driver is probably better. With a stepper motor you can make discrete steps between the positions. So you don't need an encoder.  How much torque do you need?

Some examples:

https://www.adafruit.com/product/324

https://www.adafruit.com/product/1438

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