Best Dry Food Between the Three...

I received a coupon booklet when I adopted my cat, and just noticed that there's a coupon for a free bag of dry food! My options are Authority, Good Natured, and Simply Nourish. 

Currently, my girl is on a diet of Purina One Indoor Advantage dry food (what she ate in her foster home), and Sheba wet food.

What do you suggest I try out?

If you can find the grain-free version of Simply Nourish, that would definitely be the best choice.  All of the others have grains which are hard for cats to digest.  All 3 of them are a step up from Purina though, since a specific meat is the # 1 ingredient and there doesn't seem to be as much grain in them compared to purina, and there's no by-products or Menadione (synthetic K3), all of which Purina has that isn't the greatest. Keep in mind also, these are all Petsmart exclusive brands so if you make a permanent switch to one of them, make sure you have easy access to a Petsmart location! Or there's also their website if you don't.

We abandoned Purina One Kitten kibble after she finished the first bag.  The more I read about cat food the more concerns I had about corn, wheat and soy content.  But honestly, she seemed to do well on Purina One Indoor Advantage (which is not necessarily cheap).

We switched to Purina Beyond and other CWS-free brands.  My gal has been doing well on Purina Beyond Chicken & Oat Meal, as well as Purina Beyond Superfood Blend (Herring).  Also, the ingredients in Pro Plan True Nature are appealing.  I am talking about the True Nature Chicken & Egg recipe.  The price of each of these is competitive if you use use a coupon (which Nestle Purina often provides) or buy during a sale.

I'd go with a grain free Simply Nourish as well, just looking at the ingredients and amount of protein. My cats have always been very picky about dry foods, so you may have to buy a few different kinds and brands before finding something they will eat!  I was a sales person for Nutro a long time ago and even though I tried to feed my cats that, I had to move on due to their tastes