After you broadcast the seed, it needs to be raked lightly into the surface. In order to germinate, grass seed needs light and contact with the soil, so be careful not to get it too deep. Germination will be better if you roll the seed after you rake lightly. Existing grass will act as a mulch or nurse crop for over-seeded areas. On newly seeded areas, spreading mulch will make your job much easier.
Straw is the least expensive way to cover a large area.
An average bale of straw will mulch approximately 1000 square feet. The disadvantage of straw is that it's slow to break down and often has a lot of weed seeds. Peat moss is available baled and can be spread lightly over an area to be seeded to help retain moisture. Burlap will help hold a steep grade, but is difficult to remove without damaging the grass. It can be easily removed after the grass has been in a few weeks and can be reused.