If I had to pick on in the current economic environment, I would select Brazil. They have achieved something remarkable in terms of growth and sustainability in the last ten years. They have a population of over 200 million, are energy independent and therefore not subject to the fluctuations in oil prices or supplies. They have greatly increased their manufacturing base and the middle class is growing rapidly there.
As you know, it all depends on what you want to do. This will be the key factor. If all things are equal, I would say that a place like the Philippines would be a great place. Let me give you three reasons why. First, things are relatively cheap there. So, you can save money in this way. Second, the labor force speaks English. So, communication is not a problem. Third, Asia is becoming increasingly wealthy and it might be good to have a base there for the future.
The answer to this question depends a lot on what you mean by "going international" and whether this links to business or not. There would be a whole range of questions that you would need to ask yourself as regards to whether a country is able to "go international" or not, based on factors such as the strength of that country's currency, the various products that are produced nationally and the relationship of that country with transnational corporations.
The best country to go to if you are expanding internationally depends primarily on the product being sold. The country that you expand to should have a sufficiently large population willing to accept the product and have the financial resources to buy it.
For example Nokia was very successful when they introduced their range of low-cost no-frills mobile phones in India. Apple cannot expect to sell a large number of their iconic iPhones due to several factors that does not make it affordable except to a very small number of people.
If I were looking for a country to expand into, I think I would focus on the countries of Asia, except Japan, which has a rapidly aging population and a diminishing population in general. China, Taiwan, South Korea, and other such places would definitely be places to consider, as would India. Unfortunately, many countries in Europe also seem to be facing a future not unlike Japan's.
Much depends on the products you are intending to market internationally, unless you are referring to attempts to acquire foreign firms. In either case, the best countries to get involved in are the most stable, in my opinion. There are certainly enormous opportunities created by crises in various countries in the Middle East, Africa, and these days, in southern Europe. But the risk may outweigh the possible reward. I would look for political stability, even if it meant saturated markets.
There is no such thing as a country that is best in every way. Rich countries have good infrastructure and generally have business friendly laws. However, they also have mature markets that are very hard to break into. So the answer varies depending on the product that you are trying to sell and the amount of risk you are willing to take.
In "going international" with regard to business, my first question would be in what state is another country's economy. The second question I would ask is how strong the U.S. dollar is in that country: that would indicate how far your dollar would go (if you're in the U.S.) (The same concern would exist if you were starting in a country other than the U.S.—how strong is your country's currency compared to other countries?)
There seems to be a great deal of interest in drawing companies operating in other countries back to the U.S. to strengthen the economy by keeping U.S. dollars here and creating jobs for people here. The government has been talking about incentives to keep businesses on U.S. soil. I would also look into things like this.
I would also study another country's laws with regard to foreign countries operating on their soil, and what kinds of things might interfere with being successful somewhere else. For instance, if there is civil war or there are drug wars, no matter how inexpensive labor and manufacturing costs might be, there are many more concerns that could hinder success...including not only loss of financial investments, but also life.