For starting a JIRA test instance on a local machine, the Atlassian-SDK is the way to go. This is useful for testing JIRA itself, developing and debugging JIRA plugins. The SDK is available for Windows, Linux and Mac.
See the installation guide for the Atlassian SDK. For running the Atlassian SDK properly, the Oracle Java SE Development Kit 8 (JDK) has to be installed - OpendJDK does not work!