"First world" just mean the states that were America-aligned (so by definition, the U.S. goes here).

The "world" term is stupid and nobody should use it anymore (it implies that "third world" countries are lesser than America's allies)

Developing / developed economies is what more people use nowadays, and the U.S. would be classified as developed, though a binary is still not too helpful given there are lots of in-betweeens (the big elephant in the room, China, argues it should remain classified as a developing nation because, as it turns out, there is wealth inequality there too + billionaires taking too much of the pie, so a large chunk of people still live under conditions closer to developing countries, while others say that China should be a developed nation given they have the second strongest economy)