See this for the benefits of staying - particularly the ability to get into the ruins when no one else is there - no concerns about trains or busses from/to Aguas Calientes.
That's not really the case, unless they have a separate entry/different opening times. The first visitors from Aguacalientes by bus or on foot arrive on or before opening time. So I dont see how you get the ruins to yourself. Only option for that I am aware of is coming by hike as they have a different entry.
I am not sure that the 1.300 USD plus the expensive train would ever be worth it to me. The train starts to get nice after Ollaytantambo, no matter what train you use. And I would rather spend the day visiting the Sacred Valley on my way to Macchu Picchu than take the direct train from Cusco.
In any case, do as Clyde did and get two tickets (morning / evening). And really think about toilet management.
Qhap Nan: yes also some on the road have to check which are interesting to see.
You can simply compare the bus stops for the buses connection Puno and Cusco. They hit the major sites along the road, specifically the pass, Andahuaylillas (must), Raqchi (Inca).
Pisac ok i check maybe the day with salt mines; i have 1 full day to drive outside of Cuzco
I think you need two days: Western Sacred Valley (Ollaytantambo, Maras, Moray, more). Northern Sacred Valley (Pisac) plus Templo de la Luna.
I wouldn't bother with Colca Canyon & Cruz del Condor. You can't really get a great view of the depth of the canyon and my sightings of condor were distant and fleeting.
Good to know :D I was worried of having missed out.