Have a servo follow a pot is straightforward - check the examples in the IDE, or the code given in the Servo playground example.
For better results upon reading a new analog input, read it twice, discarding the first reading.
The delay is poorly defined. It's going to be the hardest part for you to get working correctly.
How long?
From onset of movement of the pot or stop of movement?
What if the pot was moved one way, then the other way, during the delay: follow the pattern or just go to the last setting?