Arduino UNO Motor Controller

I'm looking into possibly using the Arduino UNO for a project. I have a setup with an electric motor, VFD motor controller and an encoder for counting the motor shaft rotations.
My goal is to achieve a certain amount of motor rotations, with the motor being stopped automatically after the desired amount of rotations. An ideal setup would have an easy way (such as a digital display) to quickly change the number of rotations that will be made by the motor.

Would the Arduino UNO be a good product selection, or is there another product that may better suit my needs?

Any suggestions on a visual display that can be used for modifying the count of motor rotations?
Possibly something where one number can quickly be changed by shop personnel.

What type of encoder? Does the Arduino control start / stop, direction / speed of the motor?

I plan to use a rotary encoder with with it. I don't have any particular model spec'd out yet.
For motor speed, I have the variable frequency device to maintain the motor at slow speeds.
If the system can be wired for the Arduino to control start/stop, I would be okay with it.

Based on the very rough outline you've given I don't think you should have much problem implementing it with an arduino or other sequencer. Be careful of nomenclature when working it out, eg: "encoder" could be a pulse generator which gives xx number of pulses per turn of the shaft or it could be a device which gives a number for each position of shaft rotation (in which case it is often called a "resolver").
Also keep in mind timing when counting pulses. If the arduino is doing things like serial communication in the loop function it will probably be too slow to also count pulses in the loop. In this case use the "while" or "goto" function. I did this once making a tachometer and it worked nicely.
For display look at the Adafruit LCD display and for operator input look at the Adafruit numeric keypad, although I've found the code for the keypad can become quite involved.
Beyond this all I can say is work it out in block diagram form first to get all the issues uncovered and resolved before building and coding.