I spent a year backpacking through South America in 2010.
Venezuela I would not recommend at this time due to the political situation.
Brazil is HUGE. I liked Salvador and Rio of the larger cities. There are many smaller, colonial towns that were great. The beaches were great but over packed. As others have said, a bit more dangerous than the other countries.
Uruguay is a hidden little gem of a country. Great beaches, nice people, less tourists than Brazil or Argentina.
Argentina is a must visit IMO. Buenos Aires is awesome. You could easily spend a week there and head to Uruguay for a day trip. Try to visit Iguazu Falls (I preferred the Argentinian side to the Brazilian side). Patagonia has plenty of beautiful places worth seeing. The Bariloche area is a pretty nice stop with the Lakes district and some smaller mountain towns nearby and is along the way to Chile. The Perito Moreno glacier and El Chalten/Fitz Roy are close to each other a little further south. The northern area near Salta has some awesome topography.
Chile has some of the best national parks in the world. Good hiking in Tierre Del Fuego and Torres del Paine. The Atacama desert in the North was fantastic.
Bolivia is very underrated. Lots to see and do and was the most culturally different. Salar Uyuni, La Paz, the Pampas.
Peru would be another great country to visit and I would focus on Cuzco, the Incan valleys, and Machu Picchu.
Ecuador IMO is another hidden gem.
Colombia was fantastic. I enjoyed Medellin, Cartegena, and Parque Tayronas.
My recommendation for someone visiting South America for the first time would be either Argentina or Peru, and you cannot go wrong with either of those options.