So Guam and Puerto Rico, along with the Philippines to give the simplest answer became US possessions because they were in convenient locations, and the US had so thoroughly run roughshod over the Spanish Fleet and Army was to take what they wanted from the dregs of their colonial empire.

Guam in particular was a great location in the central Pacific for use as a coaling station and naval base. Part of a chain that went from California, to Hawaii, to Guam, to the Philippines, and a balance to the US/German competition over Samoa.

Hell it was even taken officially by a bloodless transfer of power when the cruiser Charleston showed up with a convoy of troop transports bound for Manila as a side show.

While the seizure of Puerto Rico was in part supported by Cuban revolutionaries hopping to free another island from the Spanish, and part desire by the US for another secure naval base in the Caribbean to balance with the British and to serve as distant protection for the long hoped for canal across Panama. While several thousand troops were diverted from the force assembling against Cuba and landed on the island to seize it from the garrison over several weeks of start and stop fighting but not being concluded one way or the other before the end of the war.

Spain was fundamentally unable to prevent the US landing where it pleased and using its emergent naval power to full effect. The Spanish fleet suffered a terrible defeat to open the war in the Pacific when Dewey arrived in Manila Bay, while the Cuba Squadron remained blockaded in Santiago Bay before sallying out in a forlorn hope and being annihilated. And despite worries over the remaining Spanish ships raiding US ports and such the fact was that the US was now top dog in town for Cuba.