Besides what the guy before me said;
Generally speaking, breaking core vulnerabilities first is "Easier" for a first timer than breaking minor Vulnerabilities of the same type. What I mean by that is, Every type of vulnerability (Core, significant, minor) exists exactly once for each chosen group. The order in which you break Core and minor vulnerabilities determines the chosens disposition to one another. So for example if you break first minor Morality and then Core morality, then the two will grow closer, and vice versa they will start hating each other. The benefit of making them hate each other is that you get a sizable sum of EE instantly, though keep in mind if they have more than 2 of positive or negative break orders, their relationship is set in stone and you won't get anymore. Additionally chosen hating each other are less urgent about helping one another, meaning they arrive later in battle, and one of the final upgrades in the tree decreases final battle "Health" based on how much the chosen hate each other, making the final battle much simpler.
Additionally, breaking a tier 2, 3 and 4 vulnerability makes the chosen much more susceptible to that circumstance and Trauma damage type.
Also, your first goal should be the ability to field a 5EE 4 turn 2 capture commander. That is how you get the circumstance damage required to break vulnerabilities, if no one explained it to you yet.