I would recommend this order:
The Lord of the Rings presumes that you have read The Hobbit. (You may very well be able to get away without reading it, but there are clear back-references.)
The Silmarillion does not presume that you have read The Lord of the Rings, but would probably not be interesting to someone who is not already invested in Middle-earth. The Children of Húrin is a much more fleshed-out telling of a series of events from The Silmarillion, and requires an understanding of the First Age stories to appreciate.
The Unfinished Tales are exactly what it says on the tin. They contain some of Christopher Tolkien's notes about the source of the text, but are mostly readable as stories. Familiarity with The Silmarillion is essential here.
The Letters of Tolkien is a very interesting read, and could really be read almost anywhere in series. It is not, of course, a story.
You should not read The History of Middle-earth unless you are totally fanatic. It is not a series of stories, but an extended discussion of the writing of The Silmarillion, The Lord of the Rings, and some ancillary works. If you do read it, you will want to use two bookmarks, one for the primary text, and one for the copious footnotes that follow. Expect large chunks of any story you might get into reading to be removed, and replaced with a reference to The Silmarillion, The Unfinished Tales, or an earlier volume of the series. Also, the last four books are only available in the original hardback.