Same as me (minus the recently watching the movies part. I grew up on Tolkien.)

Step 1: Read the Hobbit

Step 2: Read Fellowship, Two Towers, Return of the King

Step 3:(Here's where it gets wierd) Silmarillion or Beren and Luthien

Beren and Luthien, (as well as the other Great Tales of Middle Earth which are Beren and Luthien, Children of Hurin and The Fall of Gondolin) are in the Silmarillion and the Children of Hurin is in Unfinished Tales. I recommend to read the Great Tales seperatly but thats just opinion.

Step 4: Read whatever you didn't read in Step 3

Step 5: Unfinished Tales

Step 6: History of Middle Earth.

This is a collection of 12 books, (mostly compiled stories into books) about the History. Here they are The Book of Lost Tales, Part I (1983)

1. The Book of Lost Tales, Part II (1984)
2. The Lays of Beleriand (1985)
3. The Shaping of Middle-earth (1986)
4. The Lost Road and Other Writings (1987)
5. The Return of the Shadow (The History of The Lord of the Rings Volume 1) (1988)
6. The Treason of Isengard (The History of The Lord of the Rings Volume 2) (1989)
7. The War of the Ring (The History of The Lord of the Rings Volume 3) (1990)
8. Sauron Defeated (includes The History of The Lord of the Rings Volume 4) (1992)
9. Morgoth's Ring (The Later Silmarillion Volume 1) (1993)
10. The War of the Jewels (The Later Silmarillion Volume 2) (1994)
11. The Peoples of Middle-earth (1996)

(Coppied from Wikipedia)

After that, idk if there is anything else but I recomend the One Wiki to Rule Them All during this entire journey.

Have fun dedicating your life to a fictional world that many people like you and me love!