Door goes outside to my patio.

As far as the appearance goes, the only thing that matters is the doors. Make those look like they have a connection to the other doors in the house. If that back door is typical, then black doors, black door frame and nickel hardware is a good start. I happen to like bi-fold doors for closets since they move out of the way, and don't tend to block passages.

No to open shelves. Just no.

I would remove the wall that creates the opening creating an alcove, then insert three 30” ikea pantries in that space. Drawers on the bottom, doors above. So much storage.

Excellent, I like that!

Also, thank you mad_gallica a good point to make the doors consistent- I could never do open shelving for something like that, I just meant shelves which would be behind the doors.

Personally, I would save myself about $2000 and do either a good quality bi-fold doors or just double doors in the opening you've got. Check our Elfa shelving. I converted a similar closet into a pantry using Elfa and they have designers who will plan it for you or you can do it yourself. The Container Store is where I got mine, they will install it too if you have a store near you, but it is easy to do yourself. I just did shelving across the width and added two pullout drawers under the bottom shelves. I have the similar stuff in mine, cleaning supplies, food processor, mixer, canned goods, etc. They hold tons of weight. Use the money for where it shows or a romantic weekend, which you will need by the time your reno is done. Good luck.

When we built our house we opted for a smaller coat closet and made the space that was meant for a large closet into a pantry. Like yours, it’s in the hall by the kitchen across from the hall bath. We just used regular double doors to match all of the other doors in the house. We also wired light strips inside the doorframes to pressure switches controlled by the dors so that they come on and illuminate the interior when you open the pantry.