doubt regarding Millis

You could try this:

char value = 0;

void setup()
{
  Serial.begin(9600);

}

boolean ready = false;
void loop()
{
  if (!ready){
    //first 3 seconds  
    if( millis() > 3000)
    {
      ready = true; //3 seconds has passed.
    } 
    else if(Serial.available())
    {
      Serial.read(); //clear any characters arriving early.
    }
  } 
  else {
    //After 3 seconds:
    if(Serial.available())
    {
      value = Serial.read();
    }


  }
}