Upon entering the forest, head to the right. The boy there will mention about hidden items. Now head to the field of grass to the immediate right and press A on the open patch of ground there to get a Potion. From there, head to the south to back to Route 104's separated area. Here, you can find a Poke Ball in the open field.
Return to the forest and go to the left this time. Here, you can battle a Bug Catcher looking around in the grass. After defeating him, cross the patch of grass and grab the Paralyze Heal in the corner behind him.
Bug Catcher Lyle (Prize Money: P80)
Continue to the right and follow the path until you run across a Devon researcher looking around for a Shroomish. Shortly after, a Team Aqua Grunt will appear.
Team Aqua Grunt (Prize Money: P360)
After defeating the grunt, the Devon Researcher the Exp. Share and he will also fully restore your Pokémon. Exp Share is a key item that allows other Pokemon in your party to earn 50% of the exp, even when they're not fighting.
Follow the path to the left and you'll encounter another Bug Catcher trainer. Grab the Ether in the corner along the path, then head for the exit for now. You cannot proceed to the right for now since there's thorny tree blocking the path. Just take note of its location and remember to come back for it later when you get the HM Cut.
Bug Catcher James (Prize Money: P128)