I’m assuming that you’ve already read “The Silmarillion”. If not, then start there first, then read “Unfinished Tales” after you finish “The Silmarillion”. I wouldn’t recommend buying any of the “History of Middle Earth” series until AFTER you have read “Unfinished Tales”, because the material in HoME (as it’s usually abbreviated) is even more unfinished than the stuff in “Unfinished Tales”. If you find that you don’t like “Unfinished Tales”, then you’ll know not to bother with HoME.
As to what HoME contains: it’s a hodgepodge of rough drafts, partially finished stories, essays, etc., with scholarly comments by Christopher Tolkien, who compiled it. A rough summery of the series follows:
Book of Lost Tales, volumes 1 and 2 - contains Tolkien’s earliest writings (from 1917 to the early 1930s), which are the seed from which “The Silmarillion” later sprouts. They are written in a very archaic style, are are considerably at varience with his later work. These are the LAST books to read in the series, IMHO, even though they were the first published.
Lays of Beleriand - contains partially finished versons of several poems, including the Narn i Hin Hurin and the Lay of Leithen/Tale of Beren and Luthien. Fun if you like poetry.
The Lost Road and The Shaping of Middle Earth - these contain the first drafts of “The Silmarillion”, also an extensive proto-Quenya lexicon, which is essential if you are interested in studying Tolkien’s languages.
The Return of the Shadow, The Treason of Isengard, The War of the Ring, and Sauron Defeated - these four volumes contain rough drafts of “The Lord of the Rings”; Sauron Defeated, as I recall, also contains some supplemental essays and some materials that didn’t make it into the final version of the book (including the original ending chapter for “The Return of the King”, which WASN’T The Grey Havens!)
Morgoth’s Ring, The War of the Jewels, and The Peoples of Middle Earth - IMHO, the best three volumes in the series, they contain another, later draft of “The Silmarillion”, the Grey Annals (which gives a timeline for events in the First Age), Laws and Customs among the Eldar (exactly what it sounds like) and “Athrabeth Finrod ah Andreth” (a philospohical conversation between Finrod and a mortal woman about the differing nature and fate of Elves and Men), and multilpe essays concerning the nature of Morgoth, the origin of Orcs, Glorfindel’s death and return, dwarves, languages of the Elves and how they change with time, etc - wonderful stuff. Peoples of Middle Earth also contains the original appendices for “The Lord of the Rings”.
If you like “The Silmarillion” and “Unfinished Tales”, I’d recommend starting HoME by reading “Morgoth’s Ring”, then “War of the Jewels” and “Peoples of Middle Earth”, THEN read the rest of the series (which is much harder to follow).
If you DON’T like “The Silmarillion” and “Unfinished Tales”, then honestly, I wouldn’t bother with any of the HoME series, except perhaps for the four volumes containing the rough drafts of “The Lord of the Rings” (but ONLY if you want to see how the novel evolved over time).
Hope this helps!