Bonus points for noting your "trainer type." It appears you may need to set this in both the secret base club in Fortree City (female pokemon ranger in back right) and the Pokemon Center in Rustboro City (man in a suit by the map), though perhaps Rustboro is only for link battles while Fortree is only for secret bases.
Remember, you make a better "secret pal" if you have a useful trainer type that gives access to "pick something up," which is by far the best overall ability. "Pick up stones" and even "gather berries" have some use too, at least until you've acquired a sufficient stock of evolutionary stones and accessed all the rare berries. Note that "Ace Trainer" is in fact horrible and has access to NONE of these skills. So though we may all like to think of ourselves as Ace Trainers, if you want to make your base more desirable to add, choose a different trainer type. A list of types and their associated skills is available here. If you don't want to go through the chart, Schoolkid, Beauty, and Ninja Boy are all excellent choices, with access to all three of these skills when a player's secret base reaches the Gold level.
