Not sure I completely got the question. I like herringbone tho.

If by "subway" you mean a stretcher bond (looks just like your house brick pattern) or stack bond, I would recommend something different than the house. I imagine you are picking a color close to the house red as well, close, but not quite, and that will be too much the same.

It also sounds as if you have "zones" set up and the shape will not be a single pure rectangle. If herringbone (stretcher bond as well) I would suggest separating some or all the zones with a header course.

Start with a plan sketch, as you need an accurate quantity. You also should plan for the placement of the gazebo now to make sure it is within setbacks and other size regulations.