Hi Ringsingkang,
I would definitely recommend TurBus. I used them a lot in Chile and they are a great service. To get from Santiago to the border with Peru will take you 2 days approx, assuming you aren't stopping anywhere along the way. If you have the time to spare, I would recommend busing to San Pedro de Atacama (a straight 24 hour trip from Santiago), spend a day there to break the journey and then bus from there to the border (Arica).
When you arrive at Arica (on the Chilean side) you can get a collectivo to the Tacna bus station (Peruvian side). There you show your passport and can arrange transportation to Arequipa. I would recommend travelling with Cruz del Sur bus company or Ormeno on the Peruvian side.
Hope that helps 