The Iguazú Falls are tremendous all year round, but their force depends on recent rainfall, so April is usually best. However, climate change is making the seasonal differences unpredictable here.
The Esteros are interesting all year round. The best time for seeing wildlife is spring and summer (September to April), though temperatures can reach an unbearable 45C in January. October and November are great, and so is March.
Note: flight, boat, train and bus timetables change constantly, and airlines come and go, so please do not rely solely on this information for your travel planning. Check with relevant companies, or a flight search engine like Skyscanner, first.
Puerto Iguazú is well-served by LAN, Aerolineas Argentinas and Austral flights from Buenos Aires, other cities in Argentina, and Brazil. There are also regular flights from Buenos Aires to Posadas and Corrientes, the nearest airports to the Esteros del Iberá.
Alternatively, take one of the overnight buses from Buenos Aires operated by Flechabus and Crucero del Norte, which stop at Mercedes and Puerto Iguazú. Crucero del Norte also operates services from Brazil. The buses are more comfortable than you'd expect, with reclining seats, air conditioning and toilets, and are often the easiest option for the Esteros del Iberá, as the transfer time from Mercedes is much shorter than from Posadas or Corrientes.
Bear in mind that roads in the Esteros del Iberá can become impassable after heavy rain, so check the forecast before you leave Buenos Aires.
For information on international travel to Buenos Aires, see our guide on getting to Argentina.