In my opinion, the Classic Inca Trail is the best way to visit Machu Picchu. You can take the train and bus, but you really miss out on "following in the footsteps of the Incas." I have also hiked the Salkantay Alternative Trek, but the problem with Salkantay is that you do not see hardly any ruins, only Llactapata. To make matters worse, you end you hike below Machu Picchu in Aguas Calientes and usually wind up taking the bus the next morning. It is so much better to see Machu Picchu far away in the distance and gradually see it take form as you hike to it along the Classic Inka Trail. This, IMHO, is the only way to really get to know Machu Picchu and understand it. The numerous ruins along the Classic Inka Trail teach you much about the Inkas and prepare you for grand finale when you actually reach Machu Picchu on your own, rather than by train and bus.
Basically, it is just trekking with no rock-climbing. That said, altitude sickness can be a problem and one should become accustomed to the high altitude before hiking. To help with high altitude sickness, you can take Diamox® (Acetazolamide) several days before arriving at high altitude. Make sure to consult your doctor before taking any prescription medicines such as Diamox.