What are the best ways to define success in project management and performance?

Project Management depends a lot on the type of team - is it software or marketing?

It should all start from the definition of the scope, costs, risk predictions, and tasks. In an agile approach, the project manager will plan sprints and work with the team on them. Two of the most talked about methodologies are Scrum and Lean. Where traditional project management establishes requirements before following the plan, agile starts work with what is required and clarifies the requirements as the project progresses. Here’s more info about agile: https://www.qasymphony.com/blog/agile-methodology-guide-agile-testing/

Some tools that can help you follow progress and measure the success of completion of tasks and sprints are Jira solutions, Ravetree and Hanson but there are many others that I suggest you use.