The 10/3 you have is color coded for 220VAC service. Also red, black, white wires are used for 110VAC 3-way switching circuits, such as lighting. For 220VAC, normally the red is hot, the black is hot, the white is neutral and the bare is ground. For switching circuits, the black is hot, the red is switched hot, the white is neutral, the bare is ground.
If you are wanting 110VAC, I woud get 10/3 wire that is color coded for 110VAC, black, white, green and bare. This will eliminate any errors.
You can use any colors you want as long as you know what they are and where they go electrically. Use the black for hot, the white for neutral, the bare for ground and cap-off the red. If your outlet is three pronged and has a ground screw, you can use the red for the ground prong (red substituting the for the green wire) , and the bare for the ground screw. If there is no ground screw, eliminate the bare wire. If you modify the colors, becareful because it will not be to any code.