There are probably two easy ways to decide which is the best time to go:
- Ask a travel agent;
- Look in a brochure where the highest prices will indicate the best time;
I think that you should do a lot of internet research in order to answer your questions.
We went to Argentina 18 months ago, touring round for nearly three weeks (Buenos Aires, Iguaz�, Salta, Trelew, Ushuaia, El Calafate). It was amazing. In fact, it was so good we are going again next month! Two of the most jaw-dropping sights you are ever likely to see are Iguaz� Falls (you must do both the Argentinian side and the Brazilian side) and Perito Moreno Glacier. Google for these places.
We haven't been to Peru but note that Machu Pichu is at an altitude of 2400 metres (8000 feet); one of the trips we went on in the north-west of Argentina took us to 3000 metres and my wife, who suffers from asthma, found herself short of breath.
Don't underestimate the distances you will have to travel and the time it takes. If Peru is anything like Argentina, many of the roads are dirt tracks and speeds will be fairly low.
Get one or more good guide books.
Learn some Spanish (but note that there are meny differences between South American Spanish and the Spanish of Spain)