Prof. Birch's child is waiting for a battle in Route 103. The child is May if you are a boy, Brendan if you are a girl. This will be the first battle for you against a trainer. This is the first battle between you and your rival.
Prof. Birch's child uses a different Pokémon in the battle depending on which Pokémon you selected from the Professor after the rescue in Littleroot Town. If you choose Torchic, look out for Mudkip. If you choose Mudkip, look out for Treecko. If you choose Treecko, look out for Torchic.