I stick to solid color shirts when I wear a windowpane suit or sportcoat. Much less likely to clash.
On occasion I have paired a windowpane sportcoat with a checked (similar pattern) dress shirt. It's "bold", but looks good if the colors and pattern work together.
I have not worn a windowpane jacket with a circular pattern shirt. Not saying it can't be done.
As to the shirt color? I don't know that they match. I'm not sure if they're the same shade or not so that's a tough call. I generally try to match my shirt with A) the thin border lines around the "panes" B) the inner pane color...otherwise I'm wearing a solid white dress shirt.