Overgrown lawn (18years)

Assuming it's summer where you are, I'd call your state cooperative extension office and ask them what's a good cover crop for this time of year. In much of this country, it's way too hot to start your typical lawn grasses. Or....any real farmers nearby? One of them could probably give you some tips. Plow the cover crop under at the right time, and plant your grass.

Assuming it's summer where you are, I'd wait till late summer, then spray it with glyphosate (Roundup) to kill all the existing vegetation. When it's dead, you can remove the large debris, then roto till it. Get the soil tested and apply any lime as needed before tilling. Then get it leveled out, and seed it with the appropriate grass in late summer/early fall, which is the perfect time.

Or spray it with roundup in August, then prep -n- seed in early September just like most everyone else does.

"Large" is not descriptive enough. Some people think my 1200 sg ft garden is big but my father's was over an acre. It makes a difference. If you cut it with a string trimmer I assume nothing was very large in diameter (the branbles ?) but, from what I gather, I would still rake it off rather than try to till it in. If it is an acre or more I would probably plow (if you have at least a 14" moldboard). I have plowed some stuff in but then you eventually have to disc it or till it to smooth out the furrows. I then use some old chain link fence (weighted down) to drag over it with my garden tractor to smooth it even more.