Dialing a miniaturized stargate
Fun project :)

The scope of this question is larger than can be answered here, but I'll give a few pointers to start you out.

You don't want to try to read the symbol electronically.  Instead, you want your system to be aware of the orientation of the rotating ring, and then stop the motor at the appropriate time.

A good way to do this would be to use a stepper motor.  Driving a stepper is not trivial, but it may be entertaining to figure it out.  Basically, you tell the stepper controller exactly how much to move, and then it stops the motor at the appropriate time.

An easier way, although less accurate, would be to place some sort of conducting contacts along the ring.  Imagine that you have two stationary contacts somewhere along the main (non-moving) ring.  Then you would put 38 copper disks (for example) evenly spaced along the inner ring, so that they close the contacts when the disk is spinning.  This way, by counting the contact closures, you could know which symbol is closest to the top...

Either of these methods will require a microcontroller to orchestrate things.

Sorry that I'm not going into more detail, but hopefully this will help!  My wife says that she'll buy one from you if you decide to sell them :)

Oh, and your English is impeccable!  Even if it wasn't, there's no need to apologize.

Good luck!