As a mnemonic, x, y, and z get the colors red, green, and blue as in RGB.
The grid below the plane (the "body") consists of red and blue lines because it is the x-z-plane of the "world" (the "lab").
The plane's fuselage is red as it is its x axis. Its cockpit and vertical stabilizer are green because they point upwards in the direction of the plane's y axis. The wing tips point left and right like the z axis and therefore the wings are blue.
For intrinsic rotations, the order of angles is meant to be 1-2-3 while for extrinsic rotations the order is 3-2-1. For more details see Wikipedia. You might also want to have a look at this little game.