Assuming you put in a cool season variety of grass...
You're new grasslings are going to be dealing with their most stressful time of the year. Summer. If you get hot dry weather or warm humid nights you'll want to hold back on the fertilizer, scale back your watering to an inch a week and do so at the first sign of stress and mow at the higher limit of the suggested cutting range. The part that isn't growing or germinating you may need to do better at keeping it moist or the ground could be very compacted.

Thanks for the advice.