I can at least partially answer this question, I believe.

When Spain and the US went to war in 1898, in the wake of the destruction of the USS Maine, Spain had already lost most of its colonial empire. Mainland Spanish America had become completely free by the late 1820s, what is now the Dominican Republic had variously been independent, reoccupied by Spain, and occupied by Haiti, but was by the 1890s independent as well.

Spain's key remaining colonial possessions were Cuba, Puerto Rico, the Philippines, and African territories in what is today Equatorial Guinea.

The annexation of Cuba had obsessed American politicians since the presidency of Thomas Jefferson (arguably even earlier). This is both because its fertile tropical soil was perfect for the expansion of slave plantations and because of its geographic position in the Caribbean, controlling half of both the Yucatan Strait and Florida Strait (the only natural exits to the Gulf of Mexico). Prior to the 1890s the US had attempted to purchase the island on multiple occasions, some had tried to actually invade the island (a the better part of Narciso Lopez' 1851 expedition were American filibusterers), and in the aftermath of the US Civil War American politicians had largely distanced themselves from the idea of outright annexation. This was for several reasons. First, Cuba continued to have slavery well into the 1880s while the US had just fought a hard, bloody war which ended it in the 1860s. Reconstruction politics was still mired in the legacy of slavery and deciding not to annex seemed easier, despite the potential benefits of taking over the island. Second, because the US' domestic sugar producing interests (including the annexation of Hawaii in the 1890s) meant that domestic interests were opposed to seeing one of the world's biggest sugar producers entering the market without protective tariffs. Keep in mind, this is related to the end of the silver age of sugar on the global market. If the 17th and 18th centuries were the golden age (in terms of the massive profits to be had from sugar), the 19th century was a silver age begun when Saint Domingue (Haiti) dropped out of the market due to the Haitian Revolution. However, by the end of the 19th century and beginning of the 20th, sugar production was finally catching up with demand and prices were steadily falling. The end of the silver age came in the aftermath of World War I, when the price of sugar collapsed in a crisis known in Cuba as the era of 'thin cows'. While the price would stabilize and pick up every once in a while (demand during WWII for example), it would never be the insanely profitable and expanding market it had been in previous centuries. So, back to the 1890s, domestic producers in the US had every incentive to fight to keep Cuba out of the local market.

For several of the reasons above, and perhaps some degree of corruption/bribery, 1898 congress passed the Teller Amendment which forswore the annexation of the island.

I'm less familiar with the economy of the Philippines beyond it being a key part of the Spanish trade with the "Far East". The Manila Galleons filled with fine Chinese silks, porcelains, and other goods would pass through the Philippines on the way to the Americas and from thence the goods would come to Europe. At least, in the 16th and 17th centuries. Not sure about how the economy developed in the 18th and 19th.

I'm not a specialist in Puerto Rico either, but I have read enough to understand that it was also a producer of sugar, like Cuba, though far smaller in size. It had also been the object of aspirations that it be annexed during different periods of the 19th century (in The southern dream of a Caribbean empire, 1854-1861 historian Robert May points out that some plans went as far as annexing everything all the way to Panama, others even further than that).

While Puerto Rico produced sugar, it wasn't competition the same way Cuba was. And unlike Cuba, politicians didn't move to protect it from outright annexation with something analogous to the Teller Amendment.

It should be noted that Cuba didn't get off the hook so easily either. Governor Leonard Wood controlled the island for several years, under a US military occupation which ended in 1902 only after Cuba's constitutional assembly agreed to add the infamous Platt Amendment to its constitution. The amendment was a proposal written and passed by congress in Washington which the US imposed on Cuba. It allowed the US to intervene in Cuba whenever, wherever, and for however long the US saw fit. This in practice abrogated Cuba's formal sovereignty and independence. The US would intervene at least two more times in the following decades based on this amendment, which would only be struck down in 1933 after US backed dictator Gerardo Machado was overthrown.

Louis Perez Jr. wrote a great book on how the US perceived its policy towards non-white peoples, called Cuba in the American Imagination. In it he cites a series of political cartoons, including this famous one. In it, the US personified as Uncle Same berates several dark skinned children in what looks like a class room. This is significant for several reasons. First, it shows a symbolic representation of how a contemporary American viewed themselves and their role vis a vis these new occupied territories. The US is mature, white (remember, racism is key here and even Teddy Roosevelt subscribed to the 'superiority' of the 'Anglo-Saxon race'), and male (remember, sexism is important here, in an era when women were still not allowed to vote). The occupied territories are black (racist presumption of inferiority) and children. They are infantile because a child needs the guidance and sometimes strict punishment of an adult. A child cannot govern itself. Only a harsh paternal figure can, until they're 'ready'. This also clashes with how Cuba was depicted in earlier cartoons, as Perez shows. First Cuba was a man, fighting for his honor. Then a woman who needed to be rescued from her spouse, a representation of Spain, who was abusing 'her', which necessitated Uncle Sam stepping in (again, conceptions of gender represented and helped justify political ideas). Once occupied, she was turned not only into a child but a dark child. In a racist worldview, a child can grow up to rule itself. A dark child may not, because certain 'races' were perceived to be superior and more mature, able to self-govern.

Rudyard Kipling wrote his famous poem The White Man's Burden about the US war in the Phillipines, in fact. You'll note the similarity in ideas to the cartoon above:

Take up the White Man’s burden—

Send forth the best ye breed—

Go send your sons to exile

To serve your captives' need

To wait in heavy harness

On fluttered folk and wild—

Your new-caught, sullen peoples,

Half devil and half child

Take up the White Man’s burden

In patience to abide

To veil the threat of terror

And check the show of pride;

By open speech and simple

An hundred times made plain

To seek another’s profit

And work another’s gain

Take up the White Man’s burden—

And reap his old reward:

The blame of those ye better

The hate of those ye guard—

The cry of hosts ye humour

(Ah slowly) to the light:

"Why brought ye us from bondage,

“Our loved Egyptian night?”

Take up the White Man’s burden-

Have done with childish days-

The lightly proffered laurel,

The easy, ungrudged praise.

Comes now, to search your manhood

Through all the thankless years,

Cold-edged with dear-bought wisdom,

The judgment of your peers!

In short, Cuba was given a nominal independence because of multiple domestic considerations and had to fight to break free and obtain genuine independence several decades later. Puerto Rico was occupied and the US, viewing the island as a colonial possession to be 'civilized' and paternalistically governed, saw it as incapable of self-governance. It reproduced not only the colonialist culture of the time but the lessons it had learned from the 19th century's Indian Wars, where the indigenous civilizations of North America were invaded and forced to undergo policies nominally meant to 'civilize them', as I discuss with u/Snapshot52 in this episode of the AskHistorians podcast.

I hope this, at least in part, answers your question.

Searching the archives of the sub, I was surprised to see that this isn't a question that has actually come up very often! A few very old ones which don't at all reflect the standards of the subreddit as they are today, and the only recent, relevant one I turned up was this one, courtesy /u/hahasauce. It focuses on the Cuba side, so is hardly the be-all, end-all, but I do hope it might tide you over while we wait for someone to weigh in further!

Hello everyone,

This thread is trending high right now and getting a lot of attention, but it is important to remember those upvotes represent interest in the question itself, and it can often take time for a good answer to be written.

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