Back Routine
I think it's essential to do more than just pullups or chins. If you want to work your back, do chins instead of pullups, because your biceps help you more when you do pullups. Chins is when your palms are facing away from you and pullups are when your palms are facing towards you. I believe it's good to include rows in your workout and shrugs. You also need to work your lower back as well. It's important to have a strong lower back in general. You use your lower back a lot in lifing. Here's a good overall back routine.
BACK
Deadlifts
Lat Pulldowns or Chins
Seated Cable Rows
Barbell Shrugs
I'd keep my rep ranges low in deadlifts, and high in pulldowns, rows, shrugs.