As you enter the town, your rival will take you into Prof. Cozmo’s residence. Apparently, he got kidnapped by Team Aqua/Magma, who intend to do something with the Meteorite at Meteor Cave. Okay.
There is one thing of note in here; if you bring a Deoxys to that meteorite nearby you will be able to change it’s Forme. It goes from Normal to Attack to Defense to Speed and then back to Normal, in that order as you keep changing it.
In any case, heal up in the Pokémon Center and use the Mart as usual. Particularly in the former, you can speak with Lanette, the developer of the Pokémon Storage System (different from the PSS, the Player Search System).
You can also speak with the nearby Bug Catcher to earn some Honey , an item that will attract Pokémon - often in hordes - when used in the field. You can get some once per day from him.
As for the Poké Mart, you’ll probably find it useful to buy some of the various Balls there since they are quite effective, and there’s always the Ultra Ball for general use.
To the southwest of the Pokémon Center, you’ll see a crater in the ground; examine its center to find a Nugget . In the Contest Hall, you can speak with the old man to get a Berry Blender for your Secret Base.
In the house west of there is the Pokémon Move Maniac, who you can give Heart Scales to let your Pokémon relearn moves. That’s about it for here, though.