different action based on the number of times a button is pressed

Given that your project appears to be at its start I'll throw this one out there.

It does make use of a non-standard feature of the GCC/CPP compiler included with the Arduino IDE and thus I feel fair game but it may be non portable to other compilers - the range based 'case' statements associated with the standard 'switch'/'case' pair.

#include <Servo.h> 

const uint8_t   pinSERVO    = 9;

float           pos         = 0;    // variable to store the rotary switch input
Servo           servo;

void loop()
{
    // ... 'analogRead' will return a value in the range 0 - 1023
    switch ( analogRead(A0) )
    {
        case    0 ...   99:             return;
        case  200 ...  299:             return;
        case  400 ...  499:             return;
        case  700 ...  799:             return;


        case  100 ...  199: pos =  10;  break;
        case  300 ...  399: pos =  13;  break;
        case  500 ...  599: pos =  20;  break;
        case  600 ...  699: pos =  25;  break;
        case  800 ...  899: pos =  30;  break;
        case  900 ... 1023: pos = 120;  break;
    }

    servo.write(pos);
}

void setup()
{
    servo.attach(pinSERVO);
    servo.write(pos);               // arm speed controller
    delay(3000);
}