Viridian City
Viridian City is only slightly bigger than Pallet Town, with it's own Pokemon Center, Pokemon Mart, and a Gym. The Gym is usually a busy hangout for Pokemon Trainers all over, but this one is closed (for now). The friendly citizens will gladly help you out with any questions you have. Drop by the Pokemon Center to heal your Pokemon, then head towards the Pokemon Mart. Once inside, the clerk will ask you to take a package to Prof. Oak. Run back to Pallet Town and deliver the package to get a Pokedex. As long as you're in Pallet Town, drop by Gary's house and get a map from his sister. When you return to Viridian City, stock up on Pokeballs and return to Route 1 to capture a few Pokemon. If you continue on to Route 2, buy a couple of Antidotes to cure any Poison attacks you will encounter.

Pokemon Mart Inventory
*Pokeball-----------200
*Antidote-----------100
*Paralyze Heal------200
*Burn Heal----------250

Route 2
Pokemon Found 010 Caterpie, 013 Weedle, 016 Pidgey, 019 Rattata
On your way north, you will see items on the other side of the trees, but you won't be able to reach them (not yet). Route 2 has a few Pokemon and trainers to worry about, but you should worry about the forest ahead.

Viridian Forest
Pokemon Found 010 Caterpie, 011 Metapod, 016 Pidgey, 019 Rattata
There are lots of trainers hanging around in the forest, so be sure to have at least three Pokemn in your possession. As you wander around the forest, you will find items misplaced by other trainers. You will also find, if you're lucky, a Pikachu. If you capture one, it can be helpful later on, especially if you don't have Bulbasaur.
Items found in the Forest
*Antidote
*Pokeball
*Potion