Answer: What you've done so far is good. Reseeding and removing the moss will give the new grass seed a chance to develop into a healthy lawn. Moss is usually a symptom of adverse growing conditions; too much shade, poor drainage, and acidic soil. Raking to remove the moss, and loosening the soil a bit prior to reseeding should help. If you find moss returning later in the season, mark your calendar to remind yourself to add lime in the fall. Lime takes a while but it will sweeten the soil (make it less acidic) so moss won't be so apt to grow there. Fall is the best time to apply lime because it takes several months to work its magic while it breaks down.
Lawns are generally fertilized 4 times a year in the Pacific Northwest. Use a 3-1-2 ratio of nitrogen, phosphorous and potassium (the 3 numbers on the fertilizer label) and apply in April, June, September and late November. You can use any brand of fertilizer you want, including Scott's Anytime Organic fertilizer. Apply in amounts as recommended on the label.
I wouldn't do anything else to the lawn right now. Don't add peat moss. It is acidic and you really don't need anything acidic at this point. Just water deeply once each week unless spring rains supply that amount of water. Wait until April to make your first fertilizer application.
Best wishes with your lawn!
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