It's still a bit unclear how the mechanics will work in game, but it looks really good!
Could we have a look at the interface from which we can pick the mission sets? Do you need to complete certain trees to have access to others? (such as Iberian Struggle leading to Iberian Investments)
Sure. You can choose between 3 given missions at any point, and when you click on the buttons for them they will show a description and some information about the mission. When you click "Start Mission" you will jump to the next screen, starting that specific mission. Until you have finished that mission, or aborted it, you will not be able to choose a new one.

Iberian Struggle lead to Iberian Investments, but it is one of the few examples of a mission that is hard locked by another mission. In most other cases you can sort of skip past a mission by fulfilling other conditions. E.g you can open the Magna Graecia mission by finishing the Sicily mission as Carthage, but you can also simply hold land in mainland Magna Graecia.