Here is my creation of a turn table with adjustable speed.

I've made it to look nice, since you wanna use it to show off stuff!

arduino sketch, wiring diagrams and BOM included in zip file

Overall, the used components are only standard stuff, easy to find.
I've also added a testing gear, so you can figure out the fitting on the ball bearing and eventually scale the top table for printing.

It uses either an Adafruit Trinket or an Arduino Nano, the sketch is also included.
I've wired it up by soldering the wires on to the pins but you could also use jumper cables, I believe.
You only need to solder the header pins on to the Trinket and the wires onto the potentiometer.
Oh, and I recommend removing the LEDs on the driver board and cover the red LED on the Trinket/ Nano.
When using my suggested wiring for the Nano, remember to adapt the order accordingly in the sketch, line 31!
Btw, I don't have a Nano, so I couldn't confirm the funktionality.

Have fun building!