Yup, it's an FPS. I think 3rd person view is only available on PC.
You do pick from classes but each class has unique skill trees, letting you build your chosen class to any strengths you want as you progress.
This is more of an action RPG so the story isn't that heavy. It's more about killing everything, levelling up and getting items. The multiplayer is done in such a way that you or your friends can drop in or drop out of each other's games at any time, at any point in the story. You can start a new character whenever you want, but story and level progress is tied to each individual character.
I haven't looked into the customization this time around but in the first game you could just tweak colours.