+1. Don't wear them casually. I know someone who sews buttons into his jeans to wear braces, but he also has traditional jeans wear a high rise. Braces should never be clip-on. Trousers worn with braces should have a high rise and the waist can be a little bit looser than if you were wearing a belt.Don't wear braces with anything but a suit or sport jacket. They're rarely seen unless you sit down, but don't go too wild. Generally a pair of navy braces with black leather ends is the most versatile and safe.
So of course, the shirt you will be wearing with them is a dress shirt. And the shirt should not have a breast pocket because 1) the pocket will be useless (though it shouldn't be used anyway) and 2) braces over a pocket looks sloppy. There are no rules to the colours, only your own personal taste. Red braces with a light blue shirt (you wouldn't be wearing a dark blue shirt with a suit anyway) is perfectly fine. I don't know where you'd get the idea it isn't. Patterns is up to your personal taste, but to be safe, stick with solids and vertical stripes.
And also avoid elastic braces. The back piece will always be elastic, but the front should not. Barathea and boxcloth are great materials for braces.