Add-on Skills are a mechanic that serve as a way to make your characters stronger after you reach class level caps. Gaining enough EXP at max level will reward you with Class N-EX-Cubes, which can be spent at the Class Counter to get specialized bonuses themed after each class.

Each Add-on Skill you unlock is an immediate, permanent, account-wide bonus. Furthermore, every Add-on Skill set grants a 1% bonus to EXP earned, Meseta gained, and Rare Drop Rate, up to a bonus of +10%.

You do not need to be a specific class to benefit from an Add-on Skill!

tl;dr

If you just want to put a few levels in all of them quickly before maxing them out, a subjective priority of unlock would be this order:

Bouncer (To be able to regenerate PP while using the Photon Dash/Glide)
Braver (Increase to passive Critical Hit Rate, essential for higher level weapons)
Fighter (Increase to Critical Hit damage, affects all classes)
Hunter, Ranger, or Force, depending on main weapon
Slayer (Increases Critical Hit rate against stunned enemies)
Gunner (Boosts on-hit Photon Blast build rate)
Techter (Boosts passive Photon Blast build rate)
Waker (Boosts maximum PP, lowest priority)

The most important immediate boosts to reroll for with higher rank generation methods are arguably Slayer to use your Photon Blast more often, Ranger to deal more damage with your Photon Blast, and Techter to gain extra HP and damage resist. Others are more conditional. Further information or detailed reroll information is below.

Generation

Every Add-on Skill will generate with a Main Effect and two Sub Effects. The Main Effect will always occur when generating an Add-on Skill, while the two Sub Effects will be randomly chosen.

Once you unlock a specific level in the Main Effect, that will be the lowest level it can roll at. However, Sub Effects can roll at any level, depending on the generation type used.

tl;dr

Generation

Add-on Skills by class

Hunter

Fighter

Ranger

Gunner

Force

Techter

Braver

Bouncer

Waker

Slayer