Do not worry about the fog, because it will only matter in later levels. Start out with planting Sun-shrooms and Puff-shrooms on the left side of the lawn with the occasional Sea-shroom when it recharges.
Do not waste time in planting Sea-shrooms. Plant them as soon as they recharge.
When you have enough sun, plant Peashooters on the leftmost columns without digging up Sun-shrooms (digging up Puff-shrooms are okay because they are free).
Use instant-kills when the zombies start getting too close to your house.
If the fog is too much of a problem, the player can plant Torchwoods to clear out some of the fog.