Ten days isn't much time for both. Machu Picchu and Cuzco should need 3 to 4 days and the jungle another 3 to 4 days. And 2 days Lima, the capital. So there is not much time for more.
Jungle should start in Iquitos. There are a lot of agencies around Plaza de Armas that have a programme for all needs. Alternatively you can hire a boat (as we did) and a native guide and go by your own. Here all depends on quality of guide and boat. The Amazonas is huge with many arms and diffucult in orientation.
Machu Picchu is easy. Tours every morning very early. You should visit Cuzco one or two days. And think about acclimatisation, its very high and you need your time to adopt to the poor oxigen.