the simple explanation is that the big bang cause the galaxies that were made up of the material on the outside of the "bubble" of the explosion (the stuff the universe was made up of before it became atoms and energy) to move away faster than the stuff that was closer to the center. this can be seen in more mundane explosions. anything on the outside gets thrown farther than the stuff on the inside. since there is no friction in space the material kept moving away at the same speed.

in addition. the stuff that is farthest away is the stuff that is on the opposite side of that spot where the big bang occurred. therefore it will be moving away at a straight combination of the speed of our galaxy and its speed. anything that is not on the opposite side of that spot will be neither the farthest galaxies from us or the fastest moving in relation to us.

as far as galaxies solar systems expanding, they should not be (or at least not by much) due to gravity of all the rest of that galaxy or solar system. IF its stable, it will not be expanding. why would it.

the more man learns, the more he realises, he really does not know anything.