I'd say Regression testing is the most important. After you have put in the work to ensure a systems functions will still work as desired, regression testing will let you know if that will be true or not with regards to breaking existing system functionality. This is a common cause of real-world software failures.

I would definitely say QA has the most impact in the requirements/Planning Phase. During those phases early involvement will allow QA to prevent any defects, clarify the requirements, and the acceptance criteria will be defined. Before development begins, you will have a system that's testable.

QA is essential as it protects businesses from releasing products that are not up to par, thus causing at time irreparable damage to their reputation, a decrease in growth and increase in costs. Catching issues early will mitigate these issues.