Pokémon Red and Blue/Route 1

'It's time to 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, then continue onward to Viridian City.'

Cross the Wilds to Viridian City
You begin your journey at the southern end 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 as you make your way to Viridian City. The first person you will encounter is a man who offers you a free Potion. Don't miss out on that.

Wild Pidgey and Rattata appear here at almost equal frequency (Except in Pokemon Yellow, where Pidgey are a lot more common than Rattata), 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 they're the only places you're at risk of being attacked. Just keep in mind that your Pokémon will level up faster if you participate in more fights. Even though it may not seem reasonable, you should level up your starter to Level 10. Also note that players in the Yellow Version get a better deal here, since Pikachu can fry up all the Pidgey and anyways, the Pidgey are higher leveled and therefore are basically just free experience.