The U.S. came out of the civil war still using wooden ships, and by 1891, ordered 3 steel battleships. They were successfully used in Cuba, and popularity for them increased. However, there weren't any major, significant purchases after, and the U.S. was still low on the foodchain of military powers. When did the U.S. mentality of having the most powerful military take over, and why? Been wrestling with this for a while. Thanks!
World War 2.
Before World War 2, the US was largely isolationist, and kept a small military force to defend itself from invasion. It relied on its huge geographic isolation for protection. At the start of WW2, the US had the 17th largest military in the world, behind Romania.
After WW2, the US had the largest military in the world. It's a combination of being able to out produce every single country in the world, and the fact that every other major world power was destroyed. After WW2, the US promised to protect Western Europe as it rebuilt itself, and that's when the US became the superpower it is today.
During and after WW2 the US began investing heavily in the computer field, leading up to what Eisenhower would coin the "military industrial complex." Before entering the war, the US basically made a deal with Britain where they would loan and provide aid for Britain, but in exchange the British had to allow the US to set up naval bases and take over a majority of Britain's communication networks (submarine cables, etc). Up until around this time/the end of WW2 the British Empire retained the most power in the world, but it basically gave up a lot of its' power (networks, bases) to ensure that it wouldn't lose the war. There are various shifts in power in terms of how long a power stays in power, and 1945 was around the time when the US took over the gap that the British Empire had previously filled for years.
So after the war the US now had access and primary control to the largest communication structure in the world, as well as the necessary funds to further invest into technology. As far as I know/read Britain and the rest of the world couldn't keep up with the US' race to develop computers, military technology after the war.
TL;DR US' was really the only country after WW2 with funds and the economy to heavily invest in (military) technology. Also in exchange for aid during WW2 the British gave up autonomy of their communication network to the US and allowed the US to set up naval bases around the world (mostly in parts of the then-British empire).
AS FOR NAVIES, (Sorry this is a bit disorganized) kind of what I mentioned before, the US exchanged funds and supplies for unrestricted access to the British Empire's global communication network, which consisted of millions of (submarine) cables laid around the world. Previously one would have to use the BE's cable networks to send and receive messages, which made it easy for the BE to monitor communication. But now the US is given this autonomous position in using and basically owning the network.
TL;DR (Navy) If you control the flow of information and then have the funds and economy to rapidly develop technology, you are already way ahead of any other military.
Source: I took a class last semester; 'Communication, Technology, & National Security,' and all of that info is condensed from Peter Hugill's "The Geopolitical Implications of Communication under the Seas". http://mitpress.mit.edu/books/communications-under-seas
We didn't sustain a large military until after World War 2/Korea. Before these wars we had only 0.1-.3% of our population in the military. After these wars, it hovered in between 1 and 2%, and within the last 20 years it has dropped under 1% again. I don't really know anything about major purchases but I assume they follow this trend.
After the Spanish-American war the Roosevelt Corollary was put into place which added to the Monroe Doctrine (Telling European powers that the Americas were done with colonizing, not really enforced for a while, though) it said that we would intervene when necessary (mostly in Central and South America) and this is when our military spending/size started to increase.
The US navy was a thorn in the side of other navies almost from it's inception. From John Paul Jones's moments in British waters from the Bonhomme Richard, to the war of 1812, where American Frigates decimated their british opposites, the US navy represented itself well from the get go against the British - who more often then not where the great the military of the day.
As Patrick O'Brian's fictional British Captain Jack Aubrey notes - the Brits had great commanders, but poor ships. The Americans had great commands, and great ships, but very very few of them.
The US merchant fleet was second to only Great Britian going into the Civil War. This led to a huge pool of very well trained sailors, and America's intact forests led to ships and sailors who could hold their own in battle. The commerce raiding during the civil war made it almost impossible for the American merchant fleet to do business (Insurance was impossible to get), and there was a huge steep decline in American maritime activity that really did not recover until Teddy Roosevelt revitalized the Navy with the Great White Fleet.
I disagree with some of the posts below. The US was really never all that isolationist. The US was fighting Barbary Pirates (ie, Islamic corsairs) almost immediately after the founding of the Republic. There were several large scale efforts to be build defense forts in the US after the different wars, but they were also balanced with building US navy ships designed to project power as well.
As others have noted, it really wasn't until World War II when the US navy really achieved a status that no one was able to match. The US navy developed the fast carrier task forces, which they then organized in a such way where they could project power (massive overwhelming air assaults, not just single raids against isolated targets). This was not just the Essex carriers, but the development of logistics that let the Navy stay forward projected in theater at all times. Basically the US had two floating pearl harbors that could repair, replenish and rotate ships that were a few hundred miles from the battles, rather then thousands of miles away. These fleet trains made it possible to take the largest fleet the world had ever seen, and use it far more effectively then anyone had ever used naval power before.