Thank you for your excellent recommendations. I am copying and pasting them into an Email to myself so I'll have them at hand (same for HairoftheDog's suggestions). Interestingly, I figured that Silmarillion should be next, but didn't want to go with my uneducated guess. I came to that conclusion after reading Sam and Frodo's discussion at the end of The Two Towers about the tales and adventures of the Silmarillion, how they were darker and more desperate adventures than what Frodo and Sam were experiencing, and yet they got through their "tale" and in doing so, passed on the light of Earendil for Sam and Frodo to use in the dark places.
Thanks. You folks are the best.