Route 3 is a straightforward path with many trainers. It's a great opportunity to level up your team after the Brock battle. You'll find several patches of tall grass where you can catch new Pokémon like Jigglypuff (Normal/Fairy) and Spearow (Normal/Flying). Jigglypuff can be a surprisingly strong special attacker if you train it.
There's also a Pokémon Center at the end of Route 3, just before Mt. Moon. heal your Pokémon and stock up on items like Potions and Poké Balls before entering the cave. Mt. Moon is a long dungeon with many wild Pokémon and trainers, so preparation is key.