As you progress through the main story, you will accumulate a bunch of Crystallite Fragments. These are the materials you need in order to unlock new nodes on a unit's ability board.

On the ability board, there really is no one "right" way to go - it is all about what you want that character to get first. You will eventually be able to unlock all of the abilities on the board, so it is simply a matter of deciding what to go for first.

In general, if you are ever unsure of what to work towards next, it is always a good idea to unlock as many skills as you can. Skills are denoted by special icons, so they are easy to make out in the sea of nodes. Unlocking new ability nodes to improve your stats is a good way to improve your odds of success!