I haven’t read Anthem, Player’s Piano or Logan’s Run. But the rest are all classics.
Hopefully in the intervening 20 years, the OP has got round to reading Logan's Run, but if not, I definitely recommend the first two books (the third has a few captivating moments, but is often just silly, and a disappointing example of jumping the shark).
One of the things I really loved about the book Logan's Run, is that it gave me an even greater appreciation of the movie - I always loved how unique the world of the movie was, and how the technology, and culture seemed completely alien, yet vaguely familiar (as the plot develops it quickly becomes clear that the computer running the society is operating on the basis of incomplete, and unreliable data - understandable as a culture developing in a shelter, having survived several centuries of nuclear winter), such as "Carousel" being a rationalisation of the Christian Rapture, and the Buddhist Wheel Of Life, or how much of the weaponry is either unique, or subliminally representative of "Pre-catastrophe" weapons, and it took this already interesting world, and then to legitimise Logan's cover story, completely screws him over in a way that Hitchcock couldn't have dared in North by North West.
Where the Logan of the movie is robbed of 4 years of life (30 in the movie, which was presumably commentary on particularly the entertainment industry, but also societal values at the time), and forced into living as a fugitive; the Logan of the book is on his "Last Day" and comes up with the plan to run, as a means to infiltrate the network helping those find "Sanctuary" , which he plans to destroy, and kill everyone there.
What's impressive is the way the movie distilled so many concepts of the book, into this entirely different thing, that whilst frustratingly dated now, is still visually striking, and iconic. Indeed, some of the ideas are taken much further in the movie, in a very logical way, such as the Life Clock being analogous to smartphones of today, carrying the record of our entire identity, as well as facilitating financial transactions (in the book, the Life Clock simply indicates which 3rd of your life you're in, and transactions are still made using money, which means you need a job).
The book is completely different.
There never was a "Catastrophe" .
Catastrophe (overpopulation, and insufficient food resources) was averted, by the youth themselves opting to self-euthanize on their 21st birthday.
The world in the book is very much like the world of today, albeit 300 years into the future.
There isn't a class system, where "Sandmen" are born into a life of privilege.
Everyone is born in an automated, heavily fortified creche, where they are raised, and educated by machines, until they are 7 years old.
On their 7th birthday, they are sent out into the world, to spend the next 7 years doing whatever they want (mainly travelling the globe, gaining life experience, educating themselves, and figuring out what they want to dedicate the rest of their lives to.
On their 14th birthday, they have to get a job, and become a contributing member of society, until their 21st birthday - their Last Day.
Most of the jobs we have today, are still how they occupy themselves (obviously there aren't human midwives anymore), but there is the need for a new type of job : the Deep Sleep Agent, or "Sandman".
Their job is to track, and kill anyone who fails to get themselves euthanized by the end of their 21st birthday.
And when I say kill them, that rather simplifies the fact that as much as anything, their purpose is to make a very public spectacle of a fate far worse than death in a euthanasia shop, to discourage anyone else who might be thinking of running, in search of "Sanctuary" .
To that end, the Sandman is armed with a weapon intended to subliminally tap into a collective memory of the old sheriffs six-shooter: though with each of the 6 rounds having a different function, such as a gas grenade, or an explosive round - the most feared being the "Homer" which will home in on an individual, chasing them through a crowd, and then...
Well, I'm not going to spoil it for you, but as you read the book, you'll come to dread reading each even more graphic, yet unsettling and disturbingly vague description of exactly what the "Homer" does to the victim.
Where the movie is a 70's Conspiracy Thriller, the book is Eco Horror, and a worrying number of themes, and ideas it brings up seem to either be evergreen concerns, or troublingly relevant today.
Well worth reading.