The first thing I would do is figure out what kind of soil you have,
beyond the fact that it is rocky. Grass won't grow on rocks. If you
have some half way decent soil with rocks mixed in, you can till and
remove the rocks, especially since you only have 1000 sq ft to worry
about. You can also till in some humus type material, or additional
good topsoil. You should also have the soil tested to establish the
correct PH.

On the other hand, if what you have is mostly rocks and gravel, then
you need at least 6 inchs of decent top soil, preferably 9 inchs.
Whether this can go on top of what is there becomes a grading issue.
If it can't then you need to have what's there removed.

If you wind up tilling what is there, I would use Roundup to kill all
the existing plants. Roundup is one of the safested chemicals and you
can reseed a week after application. Since you're in a hurry, you're
going to have to go with sod.