oh great....don't build up your hopes about my expertise.
Anyways, I would actually suggest (if you have time) that you read LOTR again. There are a lot of Silmarillion references that, if you catch them, will make the Silmarillion more enjoyable. After that, I'd just plunge into the Silmarillion. It's thick, but it's good. I got the tape recording from my library and read along with the narrator. This helped me not stumble over names. After the Silmarillion, I'd say read the Children of Hurin. It'll be a nice break from the thickness of the Silmarillion.
Another interesting book that I found is "Unfinished Tales of Numenor and Middle-Earth." It has some really interesting stuff in it. The last part of the book is devoted to filling in gaps in LOTR. Like telling where certain characters were and what they were doing while the actual story of LOTR was on someone else. It's a great reference book.
I am currently reading "The History of Middle-Earth" a 12-volume series detailing Tolkien's life work on Middle-Earth. If you don't want to get that involved, then I suggest you just read a couple. The Book of Lost Tales (vols. 1 and 2) give an awesome version of the Silmarillion. All it really is is the Silmarillion in fire-side form. These elves just get together every night and tell tales of the old world. It's great. Another is "The Lost Road." It is an unfinished story about time-travel (written at the same time and as a compliment to C.S. Lewis' Space Trilogy.) Even though the actual story is quite short, it is very interesting. If you want more than all these that I've mentioned, try "The Lays of Beleriand." It gives the stories of Beren and Luthien and the Children of Hurin in poetry form. Very beautiful.
If you want some small stuff (not necessarily from Middle-Earth), try "Farmer Giles of Ham", "The Adventures of Tom Bombadil", "Leaf by Niggle", and "Smith of Wootton Major."
Now that you have enough reading to last you quite a few years, I suppose I'll shut up