It's all a personal choice. Whatever you like and works for you. I use Spectracide Weed and Feed in the hose end sprayer. No mixing, no mess. Kills weeds and feeds the lawn. A thicker lawn means no room for weeds. Tried all kinds hrough the years and this works for me.
It depends on your soil. High nitrogen fertilizer‘s are the common ones and the cheap ones.
But if you need to change the pH of the soil or the iron composition then you’ll need a different composition of fertilizer.
Have you had your soil tested?
Have you called your local county extension office?
Hello a soil test would be sound advice before guessing about applications.
Soil tests are always recommended every few years. Most every speaker in my master gardeners class recommend this for optimal way to address your soil and circumstances. The box and instructions can be obtained from your local cooperative extension, unless you want your lawn service to do it.
You have to have a good soil to meet your needs to growing grass. From there you will find out recommendations to promote the grass growing conditions to include fertilize lime ( pH adjustment) aerate and seed.