I’ve moved into a new construction house. They sodded behind the house ~15 yards into the backyard. We live on a little over an acre, but the whole front yard was sodded, which leaves about 1/2 acre in the backyard that is rocks, weeds, and dirt. I was doing some research about options and wanted to see if there’s anything I’m missing. I’ve attached some pictures to show what I’m working with.

What my plan is, and I have been working on so far, is manual labor. I’ve been picking up rocks and digging up some that are embedded for a couple days now. Following getting all of the larger rocks, I was planning on tilling, using a landscape rake attachment on my riding lawnmower, and then shoveling/screening the loose dirt to remove smaller rocks. Following all of that, I was going to try to regrade the dirt to make it smooth-ish. After which I would plant a Bermuda seed, just to try to get something established that will make the yard a little nicer. I don’t need the lawn to look immaculate or anything like that, just was wanting something that we could go out and throw the ball or frisbee to the dogs, and walk around on with our daughter. There are some large boulders which I would break up with a pickaxe before trying to dig up, but is all of this realistic?

Is this going to take way longer than I anticipated (a month to a month and a half) to finish? Are there any more efficient methods to removing the rocks than what I plan to do? The soil is a lot of clay, so it may not be the best for grass, anyway. With wanting such a basic lawn, will the clay soil be fine for seeding, after the rocks are mostly removed, and the soil leveled? I know tilling can and will germinate dormant weeds seeds, but I can deal with weeds more than I can deal with barren weedy rocky dirt. TIA for any tips and advice