We did two big treks in Peru: The Salkantay Trail to Machu Picchu and the Santa Cruz Trek over Punta Union Pass near Huaraz. Prior to hiking, we took a few days to acclimatize by going from Lima to Arequipa (7,600 ft.) and then to Cusco (11,100 ft.). There are lots of interesting things to see and do in Arequipa, Cusco, and Huaraz, so taking a few days to adjust to the elevation is not boring and comes highly recommended. We felt the elevation but didn't get sick. Some tourists in our group got VERY sick and it wasn't surprising to hear they'd flown in from Lima just the day before starting their trek.
There are multiple routes to trek to Machu Picchu and they are being added/rerouted all the time so do your research. We chose the Salkantay Trail because it was supposed to offer more in terms of scenery and natural wonder. The Inca Trail is thought to have better cultural offerings.
Having only done the Salkantay, I can't compare the two, but I was perfectly happy with our choice.
We got to Machu Picchu early in the morning in order to get a limited spot to hike more of the site. This additional area was very strenuous and felt pretty dangerous at times with lots of ropes and old ladders along the route.
I loved the city of Huaraz and would love to go back. It has great cafes and restaurants and is surrounded by mountains. Our trek over Punta Union Pass had some incredible scenery and let us experience an extreme elevation of 15,500 ft.
On both treks we were given coca tea in the morning. We also bought leaves to chew along the way. There is some debate about whether the leaves help with elevation acclimatization or just with the symptoms of altitude sickness. If you don't want to use the local strategy, you should do some research on other meds or using ibuprofen or naproxen to prevent altitude sickness.