I'd be there at least an hour to an hour & a half prior to departure. Also, take advantage on their online boarding pass option. My sister did this and it saved her from having to wait to get one at the airport. All she had to do was check her bags outside at the curb and head straight for the gate. Big time saver.
When I'm flying SW, I like to be at the gate 1 hour before the stated boarding time so I can get a good place in the A line (I print out my boarding pass the night before). That means allowing half an hour to get through security, depending on time of day (at peak times, it can be longer).
Barb