Pokémon Red and Blue/Route 1

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New Pokémon available
Red Blue Yellow
Not capable of
catching Pokémon yet.

Resume your journey north to Viridian City. You can't capture new Pokémon just yet, but you can take this opportunity to build your Pokémon's experience levels. If your Pokémon enters too difficult a battle, use the Run command to escape. If it faints, head home to get a little TLC from Mom, or continue onward to Viridian City and enter its Pokémon Center.

Encounter chance
Pidgey 50% 50% 60%
Rattata 50% 50% 40%

[edit] Cross the Wilds to Viridian City

Ledge Jump
One time-saving trick is to leap off the low ledges in the ground. You can only jump from a ledge when you're moving down. Be careful not to trap yourself in grassy areas.

You begin your journey at the bottom of route #1, and must travel north. Route #1 is very peaceful, and doesn't contain many interesting features. As a result, there's not a lot of things to do on your first trip to Viridian City. One of the first people you will encounter is a man who offers you a free Potion. Don't miss out on that.

Wild Pidgeys and Rattatas abound, but without any Poké Balls of your own, the only thing fighting them is good for is EXP. Be careful that they don't wear you down, and stick with your damage-dealing regular attacks. To avoid the fights altogether, spend as little time as possible walking through the grassy areas. They're the only areas where wild Pokémon lurk, so it's the only time you're at risk of being attacked.

#16 Pidgey #19 Rattata
Pidgeys are probably the single most common Pokémon in the game, so it's not like you'll be hurting for opportunities to catch one. They're not great, but their Flying-type status can blunt Grass attacks and avoid Ground attacks altogether. Unfortunately, Pidgey doesn't learn much in the way of flying attacks until later. Spearow is likely a better choice.
Not the sturdiest, but Rattata can gain the awesome 80 base power Hyper Fang at a mere level 14, which is enhanced further by the type-matching bonus. At level 20, Rattata evolves into the stronger Raticate. Much later on, it can learn Super Fang to help in efforts to weaken a target Pokémon for capture; it will cut the target's current HP in half with each use.