I believe the most important stage is monitoring and controlling. While initiation is important, components such as time and budget can be adjusted if necessary. In regards to planning, while it is very important to plan out the project, it is just as common for delays and other things problems that come up that result in the plans changing. For this very reason, I believe that monitoring and controlling is the most important because the manager has to continuously check that status of the project and ensure that it is on track. If it is not on track, then it is their responsibilities to make adjustments. 

It's difficult to determine the relative importance of the steps of the project lifecycle because they are all necessary to complete a project. It's similar to looking at a perfectly functional four-legged chair and asking yourself "Which leg is the least important?" Each stage of the process has its place and need to be present in every single project.

Although, I do have an opinion on the question "which step in the project management life cycle is the most important to perform effectively?" In my opinion, it is absolutely vital that the planning phase is done well. The planning phase lays out the groundwork for everything in the project: the schedule, the people involved, the tasks, the scope, the finances, etc. There's a correlation between the success of a project and how well it was planned. Poorly planned projects are doomed to behave wildly, with unexpected problems occuring for many tasks. Again, all steps are important to do well, it is just my belief that planning is the most important in this regard.

While all steps of the project management cycle are necessary and important, I believe that planning is the foundation for success in a project. I often hear this saying (I'm not sure where it's from), "By failing to prepare, you are preparing to fail." Having a well-thought-out and organized plan is the foundation of a project and will make it easier to execute and close out the project. Plans can be adjusted as problems arise during execution, but that does not negate the importance of a plan. How do you know that your plan is well-defined and organized? What criteria should your plan meet?

Understanding the project management phases, every phase is necessary for the project to be complete thoroughly with a successful final project. That being said, I feel that the phase that would be the most important would be the phase where the tone of the project is set. This includes defining key objectives, forming a scope, and determining the aims of the project. This phase is the initiation phase. With major flaws in this phase or items left undetermined, a project may have severe difficulty in being completed. As room for improvement is beneficial, an abundance of unknown will leave the project scope in constant flux which does not allow the project to be effectively worked on. Furthering this idea, any key objectives that are able to be changed causes the aim to and scope to be changed throughout the project.

In short, the better the initiation phase is, the easier the rest of the project should be. While there are outliers, a strong and thought-out initiation phase will allow for a thorough planning phase and simplifying the execution phase.

I really think that the starting phase is the most important, either if it is initiation where you talk about desired final product or the first few executing and feedback because if they get your project's "style" and "vibe", it will go so much more smoothly. So it's more of a strict monitoring and trying to convey the "vibe" you want at the beginning. By the time closure of a project approached, I think it's no longer a good time to fix things (even though it's the "debugging" time basically)