To maximize trigger time, I use snap caps. They allow me to practice trigger control and getting a good sight picture. You can practice both single action and double action with them, and time spent squeezing the trigger is always good. Remember the whole safe backstop thing, triple check that you're using the snap caps and all the other safety precautions.
At the range, I'd shoot mostly your target .38s to get used to the trigger in a live fire exercise, and run a couple of cylinders of the defense loads thru near the end of the session to make sure that you're comfortable where they hit. There really is no substitute for practice to help you become familiar with the firearm.