Growth points priority: Cheer/Patience > Mastery/Focus

For faster runs of content in general, Patience would be better than Cheer, because mew may nyot be able to get the encouragement multiple times. Generally it doesn’t really matter as you’ll eventually get both.

Between Mastery and Focus, pick whichever one mew consider more useful for mew. Focus’ MP decrease means the pet can use skill more often, thus proc passives and attributes more often assuming your pet deals grey damage (should be prioritized over Cheer/Patience for classes whose vital passives proc off grey damage such as Immortal or Black Massacre). Mastery helps pets deal more damage to break spikes/cages (grey damage) or just give some extra chip damage.

Pet gems to choose: For farming: EXP +x% For dungeons: Consumable Cooldown Decreases by x%, Encourage Duration Increase by x%, Encourage Cooldown Decrease by +x% and situationally also Pet Skill MP Cost Decrease x% Because of Lord Azoth's collection buff, Consumable Cooldown Decrease isn't as needed anymore. Whether you get Encourage Duration or Cooldown depends on what mew want to use the pet for. Duration is better for shorter runs or henir speedruns, where mew can't really make use of the Cooldown Decrease otherwise. As far as Pet Skill MP Cost gems are concerned, they let your pets attack more frequently and as a result proccing certain classes' passives (specifically Immortal and Black Massacre). Take these over anything else for bossing for those classes.