Have a great time, Manchester flights are generally but I'm sure not exclusively on Sundays for weekend departures. For 18 & 21 year olds who presumably have more life in them than a wrinkly like me I would agree Ayia Napa and or Protaras centre.
Your Budget should get you a good holiday in Sept / Oct and you are wise, August is very Hot sometimes unbearably so when coupled with high relative humidity. Hope you enjoy yourselves.