I'm not the most knowledgeable person in music lit., but I can suggest a few pieces, hoping that they're about the right level of difficulty. Schumann wrote some lullabies and some "papillons" that are pretty and not complex. There is always Chopin's short and slow "Prelude in A" (Op. 28, No. 7). It's good for practicing evenness of fingering. And for flexibility and timing, the simple Bach works are the best for me. Find some of his easiest preludes or dances (minuet, gigue, allemande); his really complex compositions are beyond my ability. Since I only play classical music, I cannot suggest any good arrangers for popular music, I'm afraid, though I do have a book of John Tesh's compositions that are very easy and have a pleasing sound.
I hope that's of some use!
moonandstars, I'm always glad to spread hopefulness! I really have regained a lot of coordination through medications. But my singing voice is hard to control in pitch some days, and I haven't made any effort to overcome the problem, probably because it doesn't matter to me -- I only sing around the house, and I live alone!
My best regards,