You have the potential to do more harm with leg press due to increased weight.
People don't lift cuz they don't want to hurt their back but their backs are weak cuz they don't lift.
I will have to look it up but there are some pretty high forces placed on the lower spine and pelvis during leg press...if you actually do a full range of motion.
Perform all exercises with proper form. Progress gradually and you will have no problems.
Squats and Lunges are the best strength training exercises for runners...unless someone tells me the hip and knee joints and surrounding muscles have no use for running?...didn't think so.
Do plyos. Box jumps. Split jumps.
In order of progression: basic fundamental bodyweight movements (squatting, lunging, pushing, pulling, reaching, etc), then load those movement patterns (weight training), then use those loaded patterns in dynamic exercise (plyos...the application of a physical train, in this case strength speed and power). All of the above improves the ability of the muscle to produce force improving running economy. You can't run on hearts and lungs alone...something structural provides the locomotion
Alan