Thats the US constitution's rules on new states. Not specific. Puerto Rico is certainly eligible for statehood. I found this: " 1. A territory petitions Congress. 2. The dependent area drafts a constitution with a republican form of government. 3. Congress must approve statehood by a simple majority. 4. The President must sign the bill." from here, [link]
I know the Puerto Rican public has approved statehood, but has the territorial government drafted a State constitution, or petitioned congress yet?
"How do you think the US government will handle Puerto Rico once it does become a state?" Same as any other state. Puerto Rico is already US soil, and Puerto Ricans have been American citizens for a very long time. They have their own National Guard, and most state level functions in a territorial government.
Not much will change, except people in the soon to be 51 states, will actuall hear more about PR, because it will be relevant in national politics.