Running shoes are fine. Made the hike recently with wife, 10 & 12 year olds, all in sneakers. Stop at the park Visitor Center and buy the $2.00? Trail guide. It has some interesting observations through the hike. Ask advice for parking near the trail head. We were told to park near Thurston Lava Tube and to make the hike counterclockwise. This works great, and you can take the short jaunt through Thurston Lava Tube at the end of your hike. Short ride from here to see lava flows over road. Also visit the Jaggar Museum within the park as it's the best place to view the active Kilauea Caldera from the overlook.
Have a blast! You make me wish I was there again.