I’m interested in reading some Lord of the Rings books but I’m wondering which ones to start with having to do with History of Middle-earth.
Are they all important or can one just read The Silmarillion?
The History of Middle-earth is a twelve-volume collection of J.R.R Tolkien's unpublished manuscripts, edited and commented on by his son Christopher Tolkien.
The main goal of the series is to showcase how Tolkien developed his legendarium, and so the twelve volumes more or less go in chronological order of Tolkien's life, showing texts in the order that they were written. (Though Christopher moves some around to give individual volumes more focus.)
Due to the nature of these being unpublished drafts, and their coming from the whole of Tolkien's life, many of them are very different from his published books in style and tone, and will often have continuity problems, especially towards the earlier volumes. However, a lot of these stories are the only existing versions of various tales Tolkien referred to elsewhere.
To start with, I'd recommend you first read The Silmarillion, The Children of Hurin, and Unfinished Tales. I'm going to write this list assuming you've already read those three books.
II - The Book of Lost Tales volume 2
III - The Lays of Beleriand
"The Lay of the Children of Húrin" - A long, epic poem telling the story of the The Children of Hurin in alliterative verse. It cuts off after about 2,300 lines, shortly after Turin reaches Nargothrond.
"The Lay of Leithian" - A long, epic poem, telling the story of Beren and Luthien in rhyming couplets. Cuts off after they escape from Angband, about 4,200 lines.
V - The Lost Road and Other Writings
IX - Sauron Defeated
The unpublished "Epilogue" to the Lord of the Rings. Exists in two versions and was cut out of the final book.
"The Notion Club Papers" is an interesting work, where a fictional club of Oxford dons have dreams about Numenor (among other stuff). The stuff related to Middle-earth can all be found in Part 2.
"The Drowning of Anadûnê" is a different account of the Akalabeth, but told from the point of view of men, and so differs from the one included in the Silmarillion. Christopher includes some evidence that his father intended both versions to be canon, just told from different unreliable narrators.
X - Morgoth's Ring
"The Annals of Aman" - A history of the first age told in the form of a yearly chronicle recorded in Valinor. Tolkien intended the Silmarillion to be told through a mixture of interconnected texts, each giving a different view.
"Laws and Customs Among the Eldar" - An essay describing various aspects of elvish life.
"Myths Transformed" - A series of essays from Tolkien about drastic changes he was considering making in his later years.
"Athrabeth Finrod Ah Andreth" - An account of a philosophical debate between an elf and a human.
XI - The War of the Jewels
"The Grey Annals" - A history of the first age told in the form of a yearly chronicle recorded in Middle-earth, cuts off mid-way through the Children of Hurin. Was meant to accompany The Annals of Aman and the Quenta Silmarillion.
"The Wanderings of Húrin" - The sequel to The Children of Hurin. Goes on for a few chapters, written in a similar tone and pace.
"Quendi and Eldar" - A series of essays about elf origins and some related linguistic terms.
XII - The Peoples of Middle-earth
Silmarillion is just that; the story of how Middle-earth was created by Valar ("the gods"), what went on in the earliest days of the world, how the elves appeared and the various struggles of elves and men during the first age. This is the "golden age" of elves, pretty much, the main theme is the story of the Noldor elves in their wars to reclaim the stolen Silmarils. It is also the history from the creation of the world up to the story in The Hobbit/LotR, though there's heavy emphasis on the First Age.