All you need is the Core Book, the Errata, and the great LotR RPG community. I am, in fact, a witness of this theory, as those are the only things I have.
Of course, there are probably several of the products that could be deemed nigh-necessary! (for example, I've heard that the Moria Box is absolutely tops) But as I haven't gotten any of those, I'll leave the others to coach you on which of the extra products are the goods.