And on the topic of seed versus sod... it's basically the choice between 1.) low cost, long wait, high risk, 2.) high cost, short wait, low risk. The risk - plants are vulnerable during germination until the roots take a strong hold. They are susceptible to non-ideal temperatures and water availability. Weeds may overtake them before they are ready to fight for resources and trump the weed. Sod is already germinated so all they have to do is root to the prepared soil.
Now, there are certain species of grass that you can't start from seed so those you have to either sod or plug.
Plugging or sprigging - this is an in-between option. Lower cost, lesser risk. The problem with plugging is the bumpy result due to erosion. This can be mitigated by sanding all throughout, but this would also make it harder for the plugs to spread.
We used zoysia grass on our yard. We had 3 options - hydroseeding (quite awesome process), sprigging, or sodding. We opted to sod because of the dogs. We did not want to take away the yard from the dogs for months on end while the seed germinates or the plugs take root. Yes, it cost us an arm and a leg.