I've read all the prequel books and stories that are taking place prior to Dune (11 books and some stories). I've also read Dune to see what role these prequel books play with repect to the story of Dune.
TLDR; I can say that you need none of those books to enjoy Dune. It's been over 40 years since I read Dune and I forgot a lot about it, but now that I've read it again, I can say that what the prequel books do is that they give context to a lot of things that are happening in Dune, which might not be so clear in first instance. That said, they might also take away a bit of the surprise you might have every now and then if you did not read the prequel books.
For me personally, I like to have the background information and context, so it is a win.
The long story.
Let me share something on those prequel books in the order of time, in which they take place.
The Butlerian Jihad
The first 3 books take place during the Butlerian Jihad, when mankind was fighting the machine. In this case a big computer that controlled everything and enslaved a large part of human kind.
These 3 books explain why the impact of this era was so big that it is still felt 10.000 years later, when Dune takes place. It also tells many other stories, such as the first Artreides, the Harkonnens, who were friends with the Artreides, the invention of folding space, why Tio Holtzman was not such a big inventor after all, the origin of the Freman, the start of the Sisterhood, the first mentat, the first Suk doctor, the forming of the empire and at the end how a feud between the Harkonnen and Artreides started. This feud is carried through all the prequel stories, but there is no information of an actual feud between them in Dune.
The books cover a lot of topics (more than listed above) and are written quite well in my opinion, with each of these soties intertwining with other stories at times. It is a bit too long though. It would have been better to turn them into two books. The whole jihad part feels like it goes on too long with not much happening, but the side stories give a good idea on how things started.
The Great Schools
The next trilogy gives more information on the rise of the different "schools", such as the Bene Gesserit (just called The Sisterhood at the time), the mentats, the navigators and the Suk doctors. It takes place some 80 years after the first trilogy and also covers how the first Freman rode a worm, more Harkonnen/Artreides trouble and a big clash between rationality and emotions. This last part is also the main story and makes for the boring part of these books. The two sides are written as such extremes that it becomes impossible to relate to any of the sides. This made the books a bit of a chore for me. The side stories are more interesting, but the Harkonnen/Artreides feud feels a bit forced. Not the best trilogy of the sequels.
The Houses
The third trilogy takes place much later and focuses on Leto, the father of Paul and at a later stage also Jessica, Duncan Idaho, Guerney Hallack and Tufir Hawat. Next to that there are also side stories about the Harkonnen, how Shaddam became emperor and the role of Fenring in this. Also Rabban and at a later stage Feyd-Rautha play a role. You also learn about Pardot Kynes, who was sent to Arrakis by the emperor and his son Liet and how they worked on the plan to make Arrakis more hospitable.
Again there is a wealth of information tied together in a main story with all kinds of side stories crossing and intertwining with that main story, but the main focus is on Leto, how he became Duke, found his place and the birth of his son Paul at the end of the third book.
I liked this series the best actually as for me it gives the background information that was most useful when reading Dune.
The last trilogy is only two books at the moment as the third book will be released in a year from now. It is a book that focuses on Leto, Paul and Jessica and takes place the year before Dune. The books are not covering as many side stories as the previous trilogies. You do get to learn a lot about Paul. There is a main story arc that ties everything together, which isn't that great actually. It all feels a bit far fetched to be honest. Probably in the third book more explanation as to why the Artreides had to leave Caladan for Arrakis is provided. I'm going to read it for completeness next year.
After this I will read the rest of the Dune books, the remaining 5 books in the Dune series, the 4 additional books and some additional stories. As I only read some before I go to bed, it will probably be summer when I finish all of them