Will this toolkit be enough to get me started?

You could start with that LED chaser, since it's really simple to do. I just wrote some quick code for it, and the code is pretty basic too.

int currentLED = 2;

void setup(){
  
  while (currentLED <= 12)
  {
    pinMode(currentLED, OUTPUT);
    currentLED++;
  }
  currentLED = 2;
}

void loop(){
 int pot = analogRead(A0);
 if (pot < 26)
 {
   pot = 26; // Anything faster is way too fast for the LEDs to keep up.
 }
 
 for(int led = 2; led <= 12; led++)
 {
   digitalWrite(led, LOW);
 }
 
 digitalWrite(currentLED, HIGH);
 currentLED++;
 if (currentLED > 12)
 {
   currentLED = 2;
 }
 
 delay(pot); 
}