Well, Gene, it sounds that the first thing is a thorough site clean up. I've never enjoyed that when I had to do it, but there aren't many short cuts. I take it that there are shade trees in or very near this lawn--hence the tree branches--and that will limit the use of heavy equipment, and the depth of topsoil you can apply. That may derail one of the few shortcuts you could have done--remove the top several inches of soil, and replace it with clean topsoil.
Once the site is clean of debris, and smooth and level, I would rake in about 1/2 inch of good sifted compost, to liven up the soil, probably also with a dose of an organic high phosphate fertilizer, to stimulate the roots of whatever sod or seed you plant. Granular lime or dolomitic limestone may be needed, depending on the results of a pH test. Ask your local Cooperative Extension for the best lawn grass to plant in your area, especially mentioning your basic soil type (clay, loam, or sand) and your sun exposure. Another good thing to mention is how much wear it would receive. Note that if you have kids or dogs, a lawn to make the Governor envious will probably be impossible! : )
Seed is less expensive, and is easier to find unusual varieties, but is more susceptible to weed problems, at least in the first year or two. Sod is quick and mostly trouble-free, but you pay for your pleasures, and it may not be available in the best kind for you situation. Both ways will need frequent light watering to start, gradually watering less often and deeper until the requirements of the species and site are met.
Once the lawn is established, the best results come with deep, infrequent watering, regular feeding with an organic fertilizer, such as alfalfa meal, and regular mowing, often enough to take off no more than 1/3 of the height of the grass.

thank heavens you're a member of this site, Tugbrethil - your advice is much more suited to members in the States than what we could give.

Well, I can help with some of the general gardening knowledge, anyway!