There's a science to getting grass to take. You have to keep the seed moist, and plant no deeper than 1/8" or so. Renting a grass drill is the best way to do it, but before you have the seed down get your sprinkling system dialed in. Once the grass starts to germinate, every time it dries out I was told that you lose 50% of it.
Rye seed is cheap and good. I would find the best grass seed for your area of the country, seed at the recommended rate, and add 50%-75% of the recommended seeding rate of Rye grass too. Rye will pop up in a few days if conditions are right, then it will help keep moisture in the soil for the other grass seeds.
