I don't use a rototiller when I begin a garden, but I do use a spade. (There's no way I would get a spading fork in my soil on a first-time dig.) I shake as much dirt off the grass chunks as possible, and I stack them for use on the compost bin. Then, like many of the others, I double dig what is left.
I would take a large plot like that in stages, preparing a 5'x5' section at a time. That way, you could have a small garden ready in less than a week and another in another week. You could spend the whole summer, working one section while growing goodies in another.
Once you get a small plot dug, you can call your local extension service to find out what kind of soil you have. We have alkaline soil up here in Wyoming. When I first started gardening here, I called the County Extension Agent and asked about amendments for my soil. She told me to avoid manure at all costs because of our alkalinity.
Before planting, I like to work in peat moss on new gardens. It really conditions the soil, and working it in gives me an excellent soil texture. Then I work in about 4" to 6" compost. By the time I've dug, worked in peat moss, and worked in compost, most of the larger rocks have been removed.
What fun lies ahead for you. I would kill for a nice, sunny 15'x15' patch of virgin soil!
"Imagination is more important than knowledge." -- Albert Einstein