Some_Guy said "Sod is the way to go. By the time you seed, fertilize, water water water, reseed, water water, reseed, and water, you likely would have been better off sodding.
If you really don’t want to do sod, then look into hydroseeding.
Even with sod though you still need 4-6 inches of topsoil.
Spraying the weeds first is good advice, but how much grade do you have to work with? Are you sure you don’t need to scrape out a few inches of the gravel to make room for topsoil? This would also help with the established weeds. "
I really disagree with that statement.. your comparing thousands of dollars of Sod in comparison to buying seed, fertilizer and your water bill? We just recently built our home in the South end of town and we live on a corner lot with a lot of yard. We decided that it was cheaper to seed! Our grass not only looks better then most because of the fertilizer but it's more thicker.. Doing projects yourself can cost less, but be prepared to put your time into it.
We made a center piece in our front yard with rock and tree's, we laid down a mesh material overtop of the topsoil, hardly any weeds came up after.
Good luck!