The Silmarillion might be a bit too demanding, if all you're looking for is a bit of a background to LOTR. Tolkien actually planned such a volume, but never got around to finishing it; what's left of it is mainly collected in Unfinished Tales, which is therefore your best bet.
It's a compendium of all existing tales of Númenor before its downfall, and all the canonical histories of Middle-earth in the Third Age left at the time of JRRT's death. Plus, it has sections of the tales of Tuor and Túrin from The Silmarillion, but told in a style and scope closer to that of LOTR, therefore making them highly readable.
Of course, The Hobbit is a must, and eventually you'll have to wade through The Silmarillion, which can be a bit intimidating at first reading. You won't find much useful background info on LOTR in The History of Middle-earth series, just a very thorough account of its creation; I find the Silmarillion-related materials in HoMe to be much more rewarding.
But, again: Start with The Hobbit and Unfinished Tales. You can also sample Robert Forster's Complete Guide to Middle-earth, and Hammond & Skull's thorough book of LOTR annotations, LOTR: A Reader's Companion, published just a few months ago.
Both of those helped me a lot with my translations of Tolkien's works.