First/second/third world nations are terms that I've heard while growing up but I've never seen a list or criteria that separates the categories. Only since I looked up a list on Wikipedia was I able to find a list of countries by first, second, or third world status.
Off the top of my head, traits of a first world nation would include electricity, infrastructure, stable currency, and developed residential/commercial/industrial zones. First world countries would include the United States, Canada, England, Germany, Japan, Australia, Singapore, and Switzerland.
Third world nations would be the opposite of that. These nations would be impoverished and lack electricity, infrastructure, and developed zones. Examples of these countries would include most countries in Africa and several of the bombed and devastated countries in the Middle East.
Second world nations would be somewhere in between the two. It is hard to think of second world countries so I linked a list from Wikipedia here. This includes China, Russia, Laos, Cuba, and Vietnam.
According to Wikipedia, first/second/third world nations were terms that originated from the Cold War. First World countries were just countries that were aligned or similar to the United States. The Second World countries were the communist countries and the Third World was just everything else. Even Wikipedia admits that there is no exact definition of the terms or the list of countries.
Even when I was growing up, teachers in the school system stated that developed and developing nations was a more accurate term. Lists are available on Wikipedia and they are pretty much what you would expect. Back then, I sensed that the term developing nations was a way to be politically correct (not hurt people's feelings) because a lot of "developing nations" don't really seem to be developing.
A much more methodological approach to ranking countries might be the Human Development Index. The index itself takes into consideration life expectancy, education, and income per capita. I'm not sure how it is calculated but America ranks 8th in the world with a score of .915. It looks like Norway is at the top with a score of .944. When checking this figure, I feel somewhat different when America is criticized for being ranked lower by "whatever standard" compared to other countries. Even though our rank is lower, we scored very high.