After you defeat Brendan or May in your first battle against a Pokémon Trainer, you get your Pokédex and can go to Route 103.
In Route 102, you can catch Poochyena, Zigzagoon, Wurmple, and you have a 1% chance of encountering Ralts. In Pokémon Ruby and Emerald, you can also find Seedot. In Pokémon Sapphire and Emerald, you can find Lotad. In Pokémon Ruby and Sapphire, you can find Surskit, but it's very rare.
If you have six pokémon in your party and you catch another pokémon, it will automatically go to the PC. You can use the computer in any Pokémon Center to get pokémon from the PC or store your pokémon.
There are four Pokémon Trainers in this route. If they see you, they will challenge you to a battle. There is Youngster Calvin, who has a level 5 Zigzagoon (or Poochyena in Emerald); Bug Catcher Rick, who has two level 4 Wurmples; Youngster Allen, who has a level 5 Poochyena (or level 4 Zigzagoon in Emerald) and a level 3 Taillow; and Lass Tiana, who has two level 4 Zigzagoons (or a level 4 Zigzagoon and level 4 Shroomish in Emerald).
To the right of Youngster Allen, there are two berry trees. You can collect the berries, then plant more berries in the soil afterward. However, if the game says that your internal battery has run dry, the berries will never grow. There is also a glitch that could cause the berries to not grow even if you don't see a message that the internal battery has run dry.
South of Lass Tiana, there is an area where you can find a Potion. It looks like a Poké Ball. Check on it to pick it up.
Go west from Lass Tiana to enter Petalburg City.