If you go with Peru and Ecuador you would get a chance to see Machu Pichu and the Galapagos. One thing to keep in mind is that visiting the Galapagos can be expensive, possibly eating up half or more of your month’s budget. But the rest of the trip could be very economical.

Plus between the two countries you can see some amazing things… waterfalls, hot springs, active volcanoes, amazing beaches, rain forest, cloud forest, and of course Inca ruins (in both countries). You could easily spend a month in just ONE country and see just a fraction of what they have to offer.
References :
http://www.life-in-ecuador.com/

http://www.inside-peru.com/

Latin American countries can be done reasonably on a budget — they’re not as expensive as popular European destinations, for example — however, it also depends on where you go. Often times, all of these countries offer a wide range of accomodations: from basic rooms to luxury, so it shouldn’t be too hard to stay in a budget.

If I were to choose one of those countries, it would be between Colombia, Peru, and Ecuador.
Brazil is amazing, but I found the other three countries closer to my budget (but remember that Brazil also has its fair share of budget accomodations).
Venezuela is also beautiful, and I enjoyed my time there, but it’s not the best country for a first-time traveler to Latin America.

In short, choose one or two countries. Research them very well — learn about opportunities to explore the main attractions, along with the local cultures, and exploring the natural beauty as well.
References :
Extensive travel in Latin America.