Your plan looks good to me. We spent a lot more time in Cusco - six nights - but we were there with friends and family and that meant we had lots of social things to do as well as the usual tourism stuff. It definitely takes a couple of days to explore Cusco properly. On the tour question, some people like organised tours. In our case we've never been inclined to do that (though we are doing one in October in Thailand) - we are proudly independent travellers. However in Peru we took the advice of our new sister-in-law who is a local and took some day tours in Cusco, the Sacred Valley and Machu Picchu itself. For the most part these were organised by the concierge at the various hotels we stayed at. We would not have picked up one-tenth of the information by doing it ourselves so I would highly recommend doing some tours.
In Cusco we had a local, private tour guide who had a small, modern van with a driver so we were able to jump in and out quickly while the driver stayed with the car or moved to the end point of a walk to pick us up, etc. On the first day we spent most of the time in Cusco itself looking at churches and some museums. On the second day our guide took us right through the Sacred Valley visiting towns such as Urubamba (boy does that get you keyed up for Machu Picchu), Moray and Ollantaytambo. That was a long day with lots of walking in each of the townships but it was well worth it.
When it came to Machu Picchu we took the train from Pisac straight to Aguas Calientes. There we used a local guide arranged by the Sumaq Hotel who had many years of experience and a very good command of English. It cost us only AUD$70 for a three-hour private tour. The guide met us in the hotel lobby the night before the tour (when it was raining cats and dogs), discussed what we should bring and do and then gave us his mobile in case we wanted to cancel if it was still raining in the morning. It wound up being a brilliant, sunny day so at about 7am he met us on the bus that runs up to Machu Picchu (the bus stops outside the Sumaq if you end up staying there - otherwise you need to catch it in the township) so we arrived just as the early cloud was burning off - the perfect time to catch the best views. Our guide actually recommended not climbing Huayna Picchu for a number of reasons. If you have just one day at Machu Picchu then you want to be in a particular spot to catch the best views of Huayna Picchu which you can't do if you are lining up to climb it! Also it is quite a difficult climb as you would no doubt realise. However if you are keen to do the climb, please don't let me sway your opinion!
I'm not sure I agree with the certainty of an earlier post that one day is plenty at Machu Picchu. Lots of people told us that they enjoyed their second visit to Machu Picchu more than the first because they saw different things and had time to sit and contemplate the place. Our very experienced guide also recommended a second visit (and not paying him for it - just doing it by ourselves) and some of our fellow hotel guests even considered a third visit! Unfortunately we missed out on an encore because we had a wedding to attend and the weather then set in by the afternoon. Machu Picchu was the highlight of our trip to South America and possibly the highlight of our entire two-month DONE4. I'm not normally emotional about these sorts of things but I actually teared up when I first set eyes on it. My wife and I both found it an incredibly moving place.