I don't see how you would do Puno to San Pedro with everything you want in between in 3 days. You have to get from Puno to La Paz, LaPaz to Uyuni and then a tour.

The tours from Calama (just the airport stop for San Pedro) either end in Uyuni or you can loop back to SP. There are the very cheap ones and the more expensive ones. The cheap ones you usually arrange in Uyuni or San Pedro on the spot. Two of the better known, but more expensive, tour companies doing salt flats tours are Fremen or Ruta Verde. Cordillera Traveler is also often recommended. Out of Tupiza you have Tupiza Tours, La Torre and tours out of Tupiza are often recommended over Uyuni. You can also arrange salt flat tours from La Paz.

The thing with the cheaper tours is that the small companies often pool passengers, share drivers and vehicles, so what you get may vary, which is why you see such wide ranging reviews about specific companies and why it is difficult to get a recommendation. You can make your own way to Uyuni and book something there, but if you want one of the more expensive tours you need to book in advance and should book with a company with a physical presence in Bolivia. Foreign based companies will use them anyway. No foreign company can run those tours in Bolivia, only Bolivian companies.

The normal time to see Uyuni/REA is 3 days and two nights. The third day you transfer to San Pedro.

But you need to add the time to get from Puno to La Paz, and then from La Paz to Uyuni.

Amaszonas airlines does fly from La Paz to Uyuni most days, I wound up doing this because of strikes. It was fairly expensive. In one of those Fairchild jets (an old one) like the type that crash in the jungle.

If you are looking to price one of the shared tours and booking ahead I'd recommend contacting Kanoo, they have a physical presence in La Paz (they are travel agents, not tour operators). They don't have a huge markup and can help with the other transfers into Bolivia.

www.kanootours.com