This is an organic gardening site, so you'll never hear us recommending that you put toxic products from Scott on your yard.
Welcome to the world of healthy yards and healthy soil!
Please post a couple of photos of your yard, give us a general view of the area so we can see what all is planted there, and then take a closer photo of a patch of lawn with the weeds you're worried about. This forum willl allow you to upload small photos, but if they won't go, save them someplace like Flickr or Photobucket and post a link to them and we can take a look at the yard.
Keeping up with the neighbors is not generally a good gardening practice if they use commercial chemical fertilizer to keep a mono-culture of turfgrass in their yards. Weeds aren't the kiss of death to a healthy lawn, and many years ago, before the chemical companies created products and decided they had to create a need for their products, a standard American lawn was usually a mix of grasses and clover (which is a great nitrogen fixer in a lawn context).
Welcome to the Dirt Doctor site - take time reading in our forums, and visit the Library of Organic Information
for specific answers. You'll find that products like corn gluten meal and dry molasses are much better for fertilizing the lawn and gardens at your new home than the chemicals you mentioned above. If your soil is healthy, your lawn and garden will be healthy.