Published by Cubicle 7, The One Ring: Adventures Over the Edge of the Wild is, afaik, the most recent and most modern rpg adaptation of Tolkien's immense world. It's a relatively simple and modern game systems-wise (and you can always decide to leave off some rules to help yourself and your players ease into them later), with both the beautiful artwork and the mechanics designed directly to conjure the feel of Tolkien's writings -- including rules for making traveling long distances interesting, and rules to bring the cultures of Middle Earth alive. There's practically no need to adapt the world to the ruleset (which you'll have to face in the case of a more generic rpg): it's been done by the writers of The One Ring.
As for cheapness: You get two softcover books (one for the storyteller, one for the players) bound in a hard cover case, a set of special dice and two maps - for about $50. And you don't really need anything else to be able to play. (Sure, there are more books for the game. But they are extras. Beautiful and cool extras. ;))
One caveat: The pages of my softcover books started to get loose quite soon after my having purchased the game. As soon as I noticed it, I've switched to super-careful mode, so they're still together, but friends tell me their copies haven't weathered heavier use so well. But this really is just a minor nuisance. :)
Here's a review, in case you wanted to read more about it.
Update: There's now a Revised Edition of the game out there. From the game's official page:
The best place to start your adventures in Middle-earth is with the
revised edition of The One Ring Roleplaying Game. The One Ring
Roleplaying Game is presented as a single 336-page hardback volume
that contains all the rules and background that you need to play. This
edition of the game is completely compatible with all existing
material for The One Ring, which means that there’s already an
exciting range of supplements available ready for your adventure to
begin right away.