White windows and Black shutters.

I'd go with green or blue shutters. With green, consider lighter/darker shades of moss, sage and forest green. Hard to tell with your brick. For blue, consider classic navy or a slatey blue. Cream would also work. Basically anything will be an improvement over that orange.

With the warm brick, I'd make sure your windows are a warm color, go with a cream, not a bright white.

What's wrong with the windows? I don't understand the current trend to view windows as disposable. Mine are 100 years old. They've had storm windows added and other things to improve the air-tightness. My one replacement window is no better than the enhanced old ones.