Peru has a wealth of tour agencies. If possible, look for local agencies that will have more direct experience with the places you’re going. Most cities in Peru have many local agencies that you can easily find online, either through direct searches or platforms like TripAdvisor.
Agencies vs operators
I do not recommend specific tour operators or agencies, but I do have recommendations on how to choose one. Ask if the agency is a tour operator, meaning that they do their own tours, or if they partner with other agencies. I recommend working with operators, since they will be able to tell you who the guide will be and how much experience they have.
Look out for...
Always check that the agency has programs to give back to indigenous communities. Social responsibility is an important topic in the impoverished jungles and mountains of Peru. Agencies should also have environmental protection programs.