Puerto Rico is a department of the USA in the Caribbean and should be thought more like a commonwealth as it is not a state of the USA. You can read more on that here. To you and me what you need to appreciate is that Puerto Rico will at first feel very much like being in the USA like Miami for example. San Juan looks like Miami in its roadsigns and architecture as an example - not counting Old San Juan.
There are of course many benefits and also side effects of this special relationship - but consider Puerto Rico a country in its own right and that will help you to be more open minded.