Route 1 connects Pallet Town to Viridian City. It's a short route, but it's your first opportunity to encounter wild Pokémon. The wild Pokémon you can find here are Pidgey and Rattata. While you don't have any Poké Balls yet, it's a good idea to battle a few of them to gain some experience for your Pikachu.
There are no trainers on Route 1, but there are a few patches of tall grass. Walk through them to trigger wild encounters. talk to the various NPCs you encounter; they often provide helpful tips or lore about the Kanto region. Once you reach Viridian City, your next major objective is to deliver Oak's Parcel.