[ephermata]

This is valuable advice. The supervisor is absolutely the most important consideration. It is worth pointing out two things that are different in many U.S. universities.

1) PhDs in the U.S. in CS take between 3-10 years to finish. Less if you are in theory and have a strong set of results off the bat that align around a single area. More if you need to build something with a long cycle time, such as create a new architecture and build a chip.

The first 2-3 years will have classes and feel a little like undergrad. After that it transitions into the free-form research as the post describes. Unlike in the U.K., typically you do not have a hard stop at 4 years, and you can find teaching assistantships or other sources of funding to keep going a year or two at a time.

The good news is that you have more time with relative freedom. The bad news is depending on your advisor, it is easy to drift for years without making much progress.

2) In all the U.S. universities I know, the standard state is for you to be employed by the university as a teaching assistant or a "graduate student researcher." This has impact on intellectual property. For example, the University of California used to ask and may still ask all employees to sign a "Loyalty Oath and Patent Assignment Agreement."