Don’t know how thin your lawn is. Seeding can be done here - Chicago area - spring or fall. In fact, my preference is spring, when I’ve personally had better success. There are windows in the spring and fall that you should try to hit. Check with any garden center (or on-line I expect) to figure out yours. I’d probably aim at doing it between mid-April and mid-May. In the fall, probably early October.
My approach for filling in patches is to rake the patch hard with a dirt (not leaf) rake, so that you clear out any thatch and make furrows in the dirt. If the soil works nicely enough ad I don’t care to put in the effort, I may just rake some seed into that soil. But optimally, I would spread <1" of topsoil on the area. Then spread seed onto the topsoil, and work it in by raking lightly such that only 1/4-1/3 of the seed is visible. Some folk advise using the back of the rake.
Buy good quality grass seed for the conditions you have (sun, part shade, heavy traffic…) Make sure it is from this year, and check the contents. I suggest buying in bulk from a reputable garden center, rather than a prepackaged bag/box. It might seem more expensive per pound, but you can buy exactly the amount you want, and different types if you have sunny and shady areas.
IME, the most important step is to water it regularly. The seed needs to be moist to germinate, and the young grass needs to be wet regularly to survive. Before germination, I’ll often water morning and evening - not a lot, just keeping the soil moist. After germination a single hot/dry day can be enough to kill young grass. So for the first couple of weeks make sure that you water it at least once a day if it doesn’t rain. By the time you give it its first mow, it needs far less water.
Also, be very careful of any weedkillers or fertilizers you put down before or while seeding. Definitely don’t put down a pre-emergent weedkiller.
I don’t know what Leafgro is, but I often get a kick out of seeing folk use that bluegreen mulch stuff. Way too often, they neglect to water it, and the stuff hardens into something resembling paper-mache.
I’ve never overseeded an entire lawn. If I were going to do so, I’d do what I’ve seen golf courses do, and mix seed with sand/dirt, and spread a thin layer of that mixture. Any existing grass can grow through the thin layer of soil, but the soil will protect the seed. Of course, golf courses have equipment, materials, and labor that exceed what is likely available to a homeowner.