consider gallery styled kitchen layout.

Unless you are doing it yourself the company that does the job will lay it out for you. Don't be scared to go with custom kitchen planners because the prices are comparable to the home improvement stores. Pick someone with a lot of experience that will maximize your space. If you draw your room dimensions with doors and windows you can take it to a kitchen designer and they will draw it out for you. I had two plans drawn for mine. They didn't charge to give layout and pricing.

I would have a designer incorporate both the kitchen and the sitting area and make one large area.

I'm facing a similar issue. I would put the kitchen all along that wall, extending into the breakfast space. You could make a little peninsula/ island on wheels to move around as needed for cooking. Take a look at this photo- they put a peninsula over the step down into the family room for a little breakfast bar.

Live with the house for a whike, get to know how you live in its space. Learn the flow of it and keep looking for inspiration. Take your time, you want to do this once.

Then, after all that, it depends on your abilities. If you're the DIY type, then spend some time sketching out possibilities until you come up with something you like. Bring it to a designer and have them draw it on CAD.

I agree with the person who said to get a better answer from us, we would need a scaled drawing of the entire floor. With that, we can give you some ideas.