Best way to store and use player classes?

So I am making a game where each level the player has various options for classes. This is like 'Multiplayer Classes' in Call of Duty, although the game is totally different.

Anyways, each class has a value for several floating point variables as well as an int to index what 'power' comes with this class. Depending on the level some classes are unavailable and some classes have limited # of uses, while the rest are limitless.

In the Inspector I want the level designer to be able to attach whatever classes they wish to include in the level to my PlayerController script (which is attached to the player in every level). I want classes to be stored in the Project, such that the same class will be used in different levels (if it is present in a level it is attached to the script in the form of a variable). Every time a class is added to the script, an int pops up below to determine how many times it can be used and under that there is a field to attach yet another player class.

In the Unity tutorials thus far I haven't been told a way to create an object type that can be stored in the Project tab like this. How can I do that?

I understand that for the second part, with the Inspector, I have to create an editor script in the editor folder, which I understand most of. I'm inclined to believe what I am trying to do has been done before, is there a editor script I can look at that does something similar to this, where the number of variables of a type attached to the script can vary & increase?