Before you travel through the Viridian Forest you should head east out of Viridian City to visit this route. You'll get to battle your rival again and also have the opportunity to catch a Mankey, the only fighting type you'll have access to until you reach the Rock Tunnel later in the game. If you're patient you can also catch a Spearow, which is a great alternative to Pidgey if you're looking for a flying type for your party. Don't forget to weaken a Pokémon in battle before using a Poké Ball on it, or else it will be able to break free and you'll have to try again.
Spearows may not have a third stage of evolution like Pidgeys do, but they're a bit rarer, a bit stronger, and a lot cooler. They also start off with a bigger advantage than Pidgey versus bug types since they start with Peck, a Flying type move. If you have a Bulbasaur or Squirtle you should definitely pick up one of the Bug-Stomping flyers before you enter Viridian Forest.
Commonly found early on in Route #22, you'll find a Mankey's powerful fighting attacks to be very useful against Normal and Rock-type enemies. They learn their first Fighting-type technique, Low Kick, at Level 6. Be careful using him in Viridian Forest though, bug-type Pokémon have advantage over fighting types. You should get one if you have a Charmander, he'll have a hard time damaging the Rock-type Pokémon of the first gym.
You'll find your rival on route 22 after the first tall grass, but before the second. Your rival will only have two Pokémon, Pidgey and the starter, both at level 9. Pidgey can be easily defeated with a Thundershock (Pikachu can be found in Viridian Forest). Bulbasaur and Charmander can be beaten with Peck or Gust by Spearow or Pidgey; Squirtle can be beaten easily with Thundershock.