Newbie to gardening wants to plant a lawn

Hello All, I am new to this forum, new to owning my own house, and to gardening. I bought a house in coastal NC (New Bern, Zone 8a I think). My back yard is about .1 acre. I, and my neighbors, have many trees, and I bought Pennington Smart Seed Shade grass mix to seed with, and one bag of a sun/shade mix for the corner that gets partial sun. I also bought 5 bales of straw to cover it with, and a hand seeder. I really am only putting this down because my back yard is literally barren, except vines and tree roots, and I ripped most of the vines up. I am not going for beauty, obviously, since I bought two different mixes, but I want a yard that my kids and dogs can go out in without coming back looking homeless. I can follow the directions on the bag to get the lawn seeded, but how long after planting do I fertilize, and what fertilizer works best for shade/partial sun lawns? And how often after that should I fertilize to keep it looking as good as it will? Thanks in advance. If you even just point me to another source or step by step guide on "how to get a newbie to have a nice lawn" that would be fine.

You may want to check the timing for your zone These concepts will work, it is just the timing.
You may want to check what your soil actually needs. These ideas are based on what most lawn grasses use the most.

When the weather is really cold the lawn is not growing and the chemical reactions are not happening that will make fertilizer available to the plants. This is (around here) Dec, Jan, Feb. No fertilizer. Except: If the winter is rather mild (especially Feb) crabgrass sprouts now. So a pre-emergent that stops crabgrass is best applied now. Check your zone for the optimum timing.

When the weather starts to warm in the spring the soil is still cold. Use a fertilizer that is easily available to the plants. High nitrate, some P and K, and make sure it is one that is suggested for the cold. (Mar, Apr) If your soil has a severe lack of trace minerals, then apply some now.
There is a period in the spring when the soil is warming up, so it does not matter what sort of fert. you use, but use something, the plants are growing their fastest. Great time to apply trace minerals. (May)

When the weather gets much hotter in the summer the plants may slow down. A slow release fertilizer is fine, now, because it is so warm that even the slow release types are good. A very good suggestion is a 'fertilizer' sort of product that will encourage the soil microorganisms that will destroy thatch. Some lawns tend to build up too much, and by adding and encouraging the soil microorganisms you can go a lot longer between de-thatching. (Jun, Jul, Aug) Moderate N, P, K. moderate trace minerals if your soil tends to lack these.

In the fall the soil is still warm from the summer, but the air is cooler. Even if there are some hot days the day length is shorter, so the lawn is under less heat stress. Most cool season grasses do a lot of growing now, especially of their roots. I would use a fertilizer that has moderate N, higher P and K, and trace minerals are best now, so even if your soil has a reasonable supply, add them to replace what the lawn has used.

It sounds like the grass may have died from being shaded as the nearby trees matured. If there isn't enough light for grass to grow, fertilizer and more seeds won't help. Some other kind of mow-able ground cover might be an option, or removing some of the lower limbs from the trees, if appropriate.

For whatever might be able to be grown there, periodic applications of compost if necessary, and NOT bagging lawn clippings, so they fall back into the soil, would be a much more environmentally friendly plan than fertilizer, especially where kids and dogs play. Would you be able to add a picture of the area in question?

I'm also concerned about the ivy you mentioned. Do you know what kind? If there are still roots of it in the area, they may not be dead and may continue growing next year, or sooner.

Can you send in a picture of the area your concerned about, maybe the tree's need some lower limbs cut off to lift the over shadowing canopy which in turn, allows much needed light into the whole area, but IF that's not a great problem, then some pictures will maybe show up other problems.
Also tree's remove a lot of water / moisture from the soil therefore a lawn will have to try survive on very little rainfall or watering from a hosepipe. Again a picture could tell a lot of things like that IF that has anything to do with the dead lawn.

Kindest Regards.
Weenel.