I flew SW last March - same deal - prechecked 24 hours prior and all I had to do was show my eticket scanner thingie on my phone. A great majority of people were standing in a LONG line, taking off shoes, coats, etc.......I didn't have to do any of that. They opened the gate right at the security guy and I went through the xray your carry on baggage conveyor and was on my way. Since SW does no assigned seats, and I was prechecked, I was one of the first onto the plane and got a 2nd row seat - which meant I was off that plane in a heartbeat.
As far as the laptop goes, you generally (SW's webpage can tell you their policy, but they're all pretty much the same) can take one bag to stow in the overhead storage and one thing that can fit under the seat - obviously that's where you want your laptop. Enjoy your trip.