Very similar situation here. 28, new to handguns (shot rifles sparingly in my youth). I think the thing that helped me with actual shooting is I picked up a couple higher velocity pellet rifles about a year ago and shoot in my basement range between 100 - 500 pellets a week. Cool, calm, breath control, trigger pull. Patience.
I always hear/read people say "Treat every gun as if it's loaded." I go one step further. I "[T]reat every gun as if it's loaded, and the trigger will pull itself at any inopportune moment." This scare factor keeps me very focused whenever I handle a gun. Not paranoid or scared, just focused.
It's a little late for your specific outing but another thing I go out of my way to do, whether handling a gun or in an area where a gun is being handled, especially at a public range: make slow(ish), deliberate movements.
I always visualize the diner scene from Pulp Fiction. What's Fonzie like? Cool? That's what we're gonna be. We're gonna be cool.