It depends on where you live as to when you start seeding; kind of like planting anything else. Usually the package of seeds tells you when to plant depending on the region you live in. We started about the early fall, and personally I think one should start in the spring before it gets too too hot. I don't know exactly where you live, but for us it was cool winters and scorching summers, so we started in-between when the temps weren't in any extreme.
I wouldn't hire any tiller. Well, we didn't and it was okay. Some little spreaders (thanks for the word

) have spikey wheels so that when you push it, it makes little shallow trenches. But I don't think it makes much of a difference to till or not, especially because it looks like you need to fill in holes/patches of soil, not a totally bare lawn. A good website is: outsidepride.com