How long does it take the planning meeting?
Usually 1/2 day to 1 day max, depending on the iteration size.
The first part can be used to review, clarify and select items from the product backlog and to set a goal together with the product owner (PO) for this iteration.
The team and the product owner must attend, anyone else can but non necessarily: for example, customers or the management can be part of it.
The second part is for the team (the product owner is not necessary anymore but can remain if wished), to define how to build the selected functionalities. Here the team members sign up for tasks and estimate them.
Keep the tasks short, in case break them down. My suggestion is to have 1-8 hours tasks, so that every day you could have something complete, this has really a positive psychological effect. Smaller tasks are also easier to estimate.