Congratulations on booking the trip. You will love it.
I did a similar trip seven years ago and hiked the Inca Trail. Absolutely great trip. You don't have to be a world class athlete to hike the trail: some of areas of the trail are practically handicapped accessible. I trained by hiking several 5,000-7,000 foot peaks in NH on weekends, about a month prior to the hike. The Incas were master engineers. Getting up at 3:30 on the last day of the hike so you can see Machu Pichu as the sun rises is a memory that will last with me forever. The food that our guides prepared on the four days was outstanding. The scenery is spectacular. After four days, we took a train to Aguas Calientes and stayed one night and a hot shower before heading back to Cusco. The U.S. dollar did really well against the Peruvian currency, so it was fairly inexpensive.
We enjoyed Cusco, but three days there is certainly enough time. We hired a local cab driver named Elvis for very short money who took us to Sacsayhuaman, the Maras Salt mines (where we drank cold, delicious purple frosted drinks made from purple corn), the Moray Archeological site, and a small, native Andean village where we purchased hand made sweaters/scarves from the locals. All of these sights are worth a visit. (I think we paid him $50 American each -there were two of us-, pjus tip, and he was our tour guide for the entire day).
I had never seen such poverty as I saw on the outskirts of Cusco proper: people living in tin roofed huts, mud-based homes, etc.
The Peruvian food was pretty good, although it was laden with lots of potatoes, olive oil (perhaps corn), and a distinct, strong local spice, which may have been a Peruvian oregano. It was very strong and I didn't care too much for it. However, in downtown Cusco within walking distance of the Marriott Hotel (where we stayed) is a fantastic Italian restaurant where they bake their own, artisanal bread: I had one of the best dishes of bolognese pasta that I've ever had in my life. I was stunned at how good it was (and, I come from an Italian family).
Best of luck
As for Lima, we never left the airport so I have nothing to offer other than the bathroom I used had no toilets and no toilet seats: just a hole in the ground that I squatted over. Sorry.