Good that you're not concerned with weeds because you're going to have plenty this year. Seeding grass in the spring is identical to seeding crabgrass. Seeding grass (again) in the late summer or fall will go much better for you. I fertilize with organic fertilizer on the federal holidays because they are easy to remember. You can follow the same schedule with a chemical fertilizer but skip the 4th of July. Monday is Memorial Day, a federal holiday. Your lawn will look much better if you follow these rules. 1. Water deeply and infrequently. Infrequently means only once a week during the hottest part of summer. Deeply means for hours at a time, all at once. I am just now starting to water weekly. I water at night for 1-3 hours per zone. I used to believe that watering at night would cause fungal disease, but after many years of doing it, I have no more disease now than I used to. 2. Mulch mow at your mower's highest setting. Tall grass helps prevent weeds and looks better than short grass. 3. Fertilize regularly with the fertilizer of your choice. In my opinion the numbers don't matter as long as they are close together. If you ever get a soil test, which I almost never suggest doing, you could tune up your numbers. But unless you have a good reason to get fancy, just stick to numbers close together. 16-8-8 is much better than 40-0-0. Slow release chemicals might be better than quick release, especially if you have a tendency to overdo it. With true organic fertilizer (not "organic based") they work differently. You can use true organic any time of the year, as often as you want. And by the way I disagree with everything on Ted123's lawn seeding link. The techniques there will give you minimal germination and result in a bumpy lawn.

If I was watering 2x per week, I would do a couple weeks at every 5 days and then go to every 7 days. The scary thing about chemical fertilizers is how much to use, how often, and how to care for the lawn after applying the fertilizer. With organic fertilizer, none of that matters. You can apply a double dose every day with no water afterwards and everything will be fine. That is why I suggest it for new grass. You can't hurt anything. Once your grass is up and you are mowing it all on a regular basis (2x per week for bermuda), then you can consider a chemical fertilizer. Be sure to water it in right away after applying. Do NOT wait for the next day just because the sprinklers will come on that day. I like alfalfa for the cost and the benefit. Even after you are on a monthly chemical fertilizer plan, I would strongly suggest you supplement the chemicals with at least one app of organics per year. Without that your soil can suffer.

Since you are overseeding you want to use the starter at the very least. Starter is high in P, which is primarily for root growth, important for new grass. It is also pretty high in K, which is also important for seedlings. Most starters contain a fair amount of N as well, it depends on the brand but usually it's in the 16-25 range. If you use the starter at the full bag rate, you can use a reduced rate of the fall fertilizer to get more nitrogen if you want, but it's probably not necessary since you don't want your existing grass growing so fast and lush that it will out compete the new grass.

Likely things will be fine. Wait and see. Nothing you can do now anyway.