Get a potion and 6 pokeballs at the pokemart, you'll need them later. Now go into Gary's house and get a town's map, despite what Gary said, his sister will still give you map. Go back into Oak's lab and talk to him, he'll give you and Gary each a pokedex. Go back to Pallet town, picking fights as you go (get your pokemon to level 11). Now go northeast to the pokemart (with a "mart" sign), you'll receive Prof. Go directly up and right to that first building (with a "poke" sign on it) and go inside, go up and talk to the nurse behind the counter (yes, it's a nurse, whistle!) she'll offer to heal your pokemon, select heal.
Make your way through the route, talk to anybody you see, one guy will give you a free potion, another will tell you a "faster" way to get home. If your pokemon faint (make sure that it doesn't, run from battles if you need to), you'll be back in your house, talk to your mom and go back onto route 1. Now that you have a pokemon, go on to the bush in the north and find fights, get your pokemon to level 10. One more thing, your pokemon will grow to level 6 if you win.
If you win, you get some money, if you lose, Gary gets the bragging rights. Before you get out of the lab, Gary will challenge you to your first match, just keep on using the first move. I recommend squirtle or bulbasaur, but anyone is fine. He'll let you choose a pokemon, choose a pokeball. Oak will stop you and lead you to his lab. Go outside, now go to the very north, you should see some grass looking areas, go onto it, before you get far, Prof.
Go to the computer and access your PC, get the potion and get downstairs.