You might be wondering what red-shift is. Red-shift is the wavelength of light that is stretched. For example, the Doppler effect where sound waves moving away change the sound to a lower pitch, light moving away is slightly moving towards a longer wavelength. Big Bang is the expansion of the universe. Red-shifts supports the Big Bang Theory because the universe is expanding and it proves both ideas. CMB is radiation filling up space. It supports the Big Bang  Theory because of it being the remaining heat after the Big Bang. Objects are receding away from us because the universe is expanding. The early universe was a hot place and it expands, but the gas within it cools. So, the universe should be filled with the remaining heat. The Big Bang is the expansion of the universe. There are many different types of stars in the universe.