Answer: Early September is a really good time of year to seed lawn grass. Before fertilizing or seeding, I would suggest you run some basic soil tests to check the fertility and pH levels of the soil. The test results will tell you how much to fertilize and if you need to also add lime to correct the pH during the soil preparation phase. You should loosen the soil down at least six inches to encourage fast rooting. You might also consider working in some good quality compost to add organic matter to the soil before doing a final leveling and raking the surface smooth for seeding.
Your local Rutgers cooperative extension should be able to help you with the soil testing and interpreting the results. They will also be able to recommend the best grass varieties for your lawn based on the test results, your expected maintenance plan for the lawn and the growing conditions in your lawn.
I should also mention that lawn grass grows best in areas with full sun all day or for at least half the day including the hour of noon. If part of your lawn area is shadier than that, you may want to consider planting a shade tolerant groundcover instead of grass.
In the meantime, you may also find the following extension web site helpful in planning your lawn care this fall. You may need to cut and paste the complete url to make it work correctly.
Good luck with your new lawn!
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