After Sil, I'd suggest Unfinished Tales. Yes, they are unfinished, but they're good. Not many hobbits here, but more than in Sil! Then you can read the related works.... Book of Lost Tales 1 and 2 are the original versions of many of the stories in Silmarillion. You really have to read and enjoy Sil to 'get' Lost Tales. Some of them are bizarrely different, very few of the names are the same, it's a real interesting look at the evolution of Tolkien's mythology. One thing you will not want to miss is in Lost Tales 2 - the only complete version of the Fall of Gondolin....
The other things, like the History of Middle Earth series, are not really stories so much as writings about the stories; rough drafts here, Tolkien's notes there. It's up to you whether you find that interesting. I do highly recommend Tolkien's Letters, though. They give great insight into the man... much easier to understand after you've read LotR, though.
Hope that helps! Lovely morning here, perfect for being a hobbit!
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.