If I understood your request, you want to color the brick flower bed borders? A paint or stain made for brick and other masonry is advised. These change the color without changing the texture or ability of the brick to breath. A limewash will lighten the brick, but if you want color, you should get Romabio as this mineral paint is tintable to a color of your choice. You could also use it on the walls around your pool.

I interpretted that the brick color will stay as is, and the house will be white with black trim and some other color that won’t clash with the brick. I assume that means you want to paint the part that’s currently a mustard color. If so, what about a light/medium aqua blue that plays off the pool color?

eta: meant to say congrats on the new house!

id consider the shades of the stone before going too white with your paint, and maybe move to like an iron ore or very dark gray over black trim. I worry you will make the stone pop too much.

as to the fence, gray, off white or clad it with wood?

I would knock down the brick garden beds, not OG and painting them will just create upkeep.