here is another picture

Am I missing what state your in.

Sorry, I'm in Colorado.

Timing for planning this project is NOW! So good for you for writing NOW. Generally you will need to kill what's there, kill it again, remove what's there, level or profile it if needed (this does not mean rototilling), scatter seed, roll the seed, and water 3x per day for 3 weeks minimum.

How big an area is the back? It looks pretty large unless that is Barbie furniture. This will help decide what equipment should be used. Those terraces could lead to a lot of hand work.

Do you want grass on all the terraces?

Do you want this to be an easy yard (nice, lawn-like prairie grasses) or do you want to spend some time on it like a normal lawn?

Is there much shade? It looks sunny in that picture except for the lower right corner of the picture.

Are you opposed to chemical herbicides?

Would you be interested in an organic approach once the grass is in?