Santiago to Puno. Here's what I did, may help you think about your trip.
I was tired of Chile by the time I got up from Puerto Mott, so I got on a bus and ground through the Atacamba desert in a day, ended up in San Pedro de Atacamba (4 years ago we had to bring our own drinking water, not sure what it's like now) where I booked a 4-tour of the Salar de Uyuni. What? you ask, that's Bolivia! That's right.
When you get to the town at the end of the 1-way tour (can't recall name, but all Salar tours end in the same town) you can get a bus straight to LaPaz, then straight to Lake Titicaca (Copacabana or Puno if you like). You can continue on to Lima or the Nazca lines from Puno.