This time of year, you can't do any seeding. The best thing is to apply the basics and maintain that way going forward until fall when you can seed. Control weeds using whatever method you prefer i.e. organic or chemical preference. Keep in mind the key to a good lawn is the soil, so get a soil test and be sure to add organic matter like compost, compost tea, molasses, fish hydrolysate, etc. I doubt you need to add any topsoil, just whatever amendments the test recommends.
The basics are the proper methods of:
You don't want to remove more than 1/3 at a time and that's the reason you have to do it gradually to get it down to maintenance height of 3 inches or slightly higher. Chopping it off all at once is called scalping, and you don't want to do that or the grass will become stressed, damaged, and vulnerable to disease.
Fertilize right now. It's not something you want to do in June or July when the weather is hot. Other than fertilizer, recommendations per soil test can be applied any time, such as lime/sulfur/etc.