I'll weigh in on this one as well, since I've read practically all the History of Middle Earth series, etc. and can give an assessment of what's contained in them.
First off, let me second the previous responses and encourage you to have a go at the Silmarillion. This gives you the "prehistory" of the creation of Arda (the world in which Middle Earth exists, in case you didn't know) and about as much of the history of the First and Second ages as you are ever going to find. There's some good stuff in there, stuff that is only hinted at in the Lord of the Rings. The tale of Beren and Luthien. The tale of the Children of Hurin. Tuor and the Fall of Gondolin. Earendil the mariner. It's a bit dense and archaic in language. It reads more like myths or La Morte De Arthur than a modern novel (like LotR), but if you can get over the different feel, there's plenty of good stuff in there.
Unfinished Tales also contains some good stuff, in the form of uncompleted manuscripts for Tuor's arrival in Gondolin, and the Narn i hin Hurin, and a story based in Numenor. There's some useful Third Age stuff in there (like the battles at the Fords of Isen, where Theodread died) and some stuff on the Palantiri and the Istari. If you can manage the Silmarillion and you still want more, go for this book.
The History of Middle Earth series is a different beast entirely. It's more the History of How Tolkien Wrote About Middle Earth. It can be very interesting to read how the stories grew and evolved as he changed and revised him, and there are uncompleted bits of stories which appear in the Silmarillion in lesser detail, along with information and insight into how the world of Middle Earth "works" (marrage customs of the elves? it's in there. Where the orcs came from? that too, in many different versions as JRR tried to reconcile their natures and origins). It can be a worthwhile read, but unless you really have an interest in how the stories about Middle Earth were developed, you'll probably have to wade through lots of commentary that would be of little interest.
I'm glad that the movies have motivated you to pick up an excellent and timeless book. Read on, my friend.
-Chris Landmark
"Was entstanden ist, das muss vergehen. Was vergangen, auferstehn." -Klopstock & Mahler
"Only liberals really think. Only liberals are intellectual. Only liberals understand the needs of their fellows." How much viciousness lay concealed in that word! Odrade thought. How much secret ego demanding to feel superior. - Heretics of Dune