All righty.  Leave out Peashooter and Tangle Kelp, and bring Potato Mine and Squash instead.

Right off the bat, plant a Sunflower (duh).  Keep planting as many of them as you can.  When the first few zombies show up, plant Potato Mines and Squashes waaaaay in front of them.  They'll die on impact with either of those plants.  This should buy you enough time to get 10 Sunflowers up (4 in back on each side, two in pool).  Once you've got the Sunflowers, start planting Wall-nuts ad try to get a Repeater in every row.  You'll especially need Wall-Nuts in the pool.  Plant Snow Peas to back up the Repeaters, and make sure the Wall-Nuts are far up the lawn so the pole vaulters won't have time to get anywhere after they jump.  Plant a second row of Repeaters if you have time.

Good luck.

By Beginning Strategy, I assume you mean Sunflowers followed by Peashooters, right?  Yeah, that'll get you be most of the time, but Peashooters can't deal with Bucket Head Zombies very well while a Repeater and a Snow Pea can easily handle one between them.  A Repeater costs exactly as much as two Peashooters, so you can save yourself some time and space by planting only them.  Besides, the extra Sunflowers you need to get them going inevitably help out later on.  Having ten or more Sunflowers is always a good idea.