Thats an ok list, but its missing a few important exercises, and its helpful to give an idea of priority. Romanian and stiff-legged deadlifts are missing. I wouldnt bother doing anything with machines for my back at all.

Heavy deadlifts
Heavy Rows, dumbell or Barbell.
Heavy shrugs

Would be (and is) my back routine. Id mix it up with Romanian and SLDLs in place of deadlifts, and chin or pull ups in place of the rows, especially if youre a big guy. Good mornings, Kelso Rows, and overhead DB Kelso shrugs would be in the mix too, for lighter work.