1. General principles:
Generally speaking, regular script is the foundation. It is easier and more convenient to practice running script after practicing regular script. But it also varies from person to person, and there is no absolute order. You can practice both at the same time, or you can practice running script first and then regular script. There is a close connection between various writings, and they influence each other and compensate for each other.
2. Specific explanation:
Regular script and running script can be practiced together. The practice of regular script is mainly to lay the foundation for running script. When you can thoroughly master the structure of the copybook, you can practice running calligraphy. For example, take a piece of white paper and write casually on it. When you can make the intervals between each word equal and not too "crooked", you can start writing running script.
There is another way, you can start directly from running script. This method is quick, but if you want to improve later, it will be difficult and you have to go back to regular script practice. But most of us practice calligraphy just to cope with daily writing. In fact, the fonts only need to be "readable".