I want to decorate my castle's gallery room with paintings of different types. Does the color of the wool affect the painting, or is it just random.
No, paintings are created randomly when you place it on a surface, so the type of wool doesn't matter.
If you don't like the painting after placing it just break it, collect the painting item that drops, and place it again: Minecraft will again randomly choose a painting that fits the space. You can keep repeating this until you get a painting you like.