Good Day!

This is my first non rev trip to london. I am leaving the week after the 4th of july and returning on the 12th. I just wanted to know what is the best and most inexpensive airline to fly out to/from london? I work for southwest so i can fly to wherever airport i need to go to fly out to london. Also..is it easier to fly into gatwick than it is to heathrow? I heard that heathrow is a mess. thanks!