Don't use concrete. Custom steps
Concrete will limit all aspects.
Pavers and retaining wall block.
Get more ideas. It's easy fix.
What's Ur budget.

Looks like you have a good space for lots of different options. Take a look at some of my pictures and let me know if anything speaks to you. I am sure we can find something you will love. Thank you

You asked how wide should the stairs be. Well pathways are at a minimum 3.5-4' wide for one person. For two people to fit 6'-8' is acceptable. I would suggest softening up the large forms of concrete with wood stairs. Possibly like in the attached pic. Or you could do a floating stair attached to a wall like in the pic below. This will need rebar and structural detailing so if you are working with a contractor he should do it for you.

You are going to need a railing back near the house and the stairs should probably go more toward the larger upper patio. While you fill in with a few large containers in the (garage) corner of the lower patio.