I think your initial question would be difficult for a historian to answer without giving a kind of non answer, so I'll try to walk you through my thought process. I'd begin by stating that the periodization of the 20th century isn't very popular with historians today. This is how you get with misnomers like "The Dark Ages" or the increasingly unpopular "Industrial Revolution."
First off, why periodize in the first place? What do you gain from periodizing time? Obvious benefits include easier memorization and an understanding of chronology. But we must consider what we sacrifice or lose by periodizing time. By diving events up we lose the sense of interconnectedness of events. The American Civil War did not simply happen in 1861, and discussing it isolation as a period alone isn't terribly insightful. It didn't just magically end on 1865 either, so discussing it as a period from 1861-1865 is out. You can add the Sectional Crisis to the beginning, and Reconstruction to the end pushing it to 1850 to 1877, but now its getting pretty large. And how did the Sectional Crisis begin anyway? This can go on forever. The end result is that I don't think this kind of periodization adds much except broad understanding of chronology.
That said, we have to start and end a discussion of events somewhere don't we? Every history class doesn't begin "In the Beginning..." So lets look at American History. It is pretty common to divide the era up into a pre-Civil-War (1760ish-1877) and post-Civil-War (1877+) as a means of cutting down on how much we discuss in class or specialize in. I don't think that particular periodization adds a lot to our understanding of American history. It just provides a start and end to a discussion. But even this periodization isn't the end all be all. There are plenty of legitimate arguments for clumping in the Civil War with the later half of American history, or extending American history back further into pre-Revolutionary times, or to cutting off the second half with WW2 or even before WW2.
There are other downsides. This kind of dividing of time will invariably be biased towards one or another nation or ethnicity, and the years will never match up neatly to make the dividing useful anyway. Most European studies don't cut the 19th century in half at all because they aren't terribly concerned with an American civil war. In fact they usually discuss what is called the "Long 19th Century" that runs from 1789-1914. Greater problems arise the deeper you dive. The 1820s in the United States, so called the "Era of Good Feelings" which really ran from about 1817 to 1825, are very different from the 1820s of France which is called the Bourbon Restoration and ran from 1815 to 1830. Not only is the character of the time different, but they are periodized differently chronologically.
If I just wanted a memorization tool, I'd probably stick with Presidential terms while incorporating some of the more benign presidencies into others. "Jacksonian America," or more accurately the "Era of the Second Party System," for example, could run from 1828 to the beginning of the Sectional Crisis in 1850. You could also use broader concepts like "Antebellum America" for the 1789-1850 or so, and "Sectional Crisis" for 1851-1865," and so on (Reconstruction, Gilded Age, etc). There are so many ways to cut the cake I can't decide on one! And even this only works on American history.
The dirty thirties? When was that started?.....
The 1890s were sometimes known as the 'Naughty Nineties'. Interestingly enough, I can't think of any nicknames like this for more recent decades, so I'd say it was a trend of the late nineteenth and early twentieth centuries rather than of the twentieth century (though I could be forgetting something).
You might be interested in the recent Monday Methods post on periodization. You've skirted some of the issues in confining yourself strictly to the west, but there are still some good rationales for not periodizing at all unless it's necessary for a specific discussion.