Travelling overland in Peru?

We actually have a trip called the Andes and Altiplano which covers exactly all the areas you identified - take a look to get a day-by-day break down of what the trip includes.

I know you mentioned travelling overland from Lima to Cusco, but this is an exceptionally long and gruelling journey by road (about 20-24 hours) and the best option really is to fly (1 hour and 20 minutes). The altitude shouldn’t be anything to worry about, we book this for all our clients all the time. We normally recommend to take the first few days in Cusco relatively easy to give you time to acclimatise. If you are really worried about the effects then we could transfer you from Cusco airport to the Sacred Valley straight away (about 1.5 hours by road) where the altitude is a couple of hundred metres lower. You could spend a few days in the Sacred Valley, before visiting Machu Picchu and then head back to Cusco once you’ve acclimatised. From Cusco you could then take the wonderfully scenic Andean Explorer train to Puno and Lake Titicaca or travel along the same route by a comfortable tourist bus.