I think the berry picking is later in the game, and everyone has to have a dodrio. I'll find out soon. But if you just battle or even run around with a meowth, he'll get a whole bunch of berries as long as you keep checking and taking the stuff when he gets it. I've also gotten nuggets, PP up, and other stuff. Remember, you cannot allow him to evolve into a Persian, b/c then he'll lose pickup! And you can crush the berries with a friend to make powder, and trade it for medicine/nutrients from the guy who gave you the berry jar. All people must have at least 1 berry to do it. Just push A as fast as possible, it's easy.
I got all the Pokemon a person could dream of, and still working on more. If you need to know the truth, seek it out here, as I am obsessed with answering all the questions I can as best I can. I can verify Event Pokemon, too! My collection keeps growing!