The gateway to the Amazon in Peru on the Amazon River is Iquitos. This is in the northern Amazon Rainforest. The northern Amazon Rainforest has a less developed tourism industry than the south and in the south Amazon Rainforest you can find many tourist lodges in the Manu and Tambopata conservation areas. I prefer the less developed nature of the north and tour operators seem to give you a more personal experience.
The main jumping off points for the Peruvian Amazon are the city of Iquitos (famous for being unreachable by road), Tarapoto (less known than Iquitos and possible has access to better deals on tours), Cusco (for the most pristine park in Peru, the Manu National Park), and then the small town of Puerto Maldonado (easily accessed from Cusco for the Tambopata Reserve).