If you still remember what happened in Fellowship, go for Two Towers then Return of the King. You don't necessarily need to re-read The Hobbit, there's a recap at the beginning of Fellowship (though The Hobbit is a great book that I would never tell you not to read again).

Personally, I couldn't really get into The Silmarillion (its too dry, I read about a chapter and a half before I got bored with the writing style compared to Tolkien's other works), even though it has a lot of information about previous ages before the third era. I still hope not to discourage you on that one though, it has merit (its just kinda boring, and I don't think that's a particularly rare opinion).

I have no input on Unfinished Tales or anything else, I've really only read The Hobbit and most of LotR (which I am most of the way through, but am currently taking a break from just because of how long and academic it is. I will finish though, my intro to the series was the movies from 20 years ago, so I mostly know what happens already).