With your Pokédex and Poké Balls in hand, head back to Viridian City. Now you can proceed north to Route 2. This route is relatively short and leads directly to Viridian Forest. You'll encounter a few patches of tall grass where you can catch Pidgey and Rattata, similar to Route 1.
Before entering Viridian Forest, make sure your Pikachu is well-rested and you have a few Potions. Viridian Forest is your first real challenge, featuring wild Bug-type Pokémon and several trainers. It's a good place to start catching Pokémon and gaining experience.