Must-see/read: The first two movies, "Only You" and "Beautiful Dreamer" (the latter, especially); the first OAV, "Inaba the Dreammaker"; and the fifth movie, "The Final Chapter". The first few issues of the manga (and the anime, if you're interested, though the animation is sub-par), to see how it all starts. I haven't read much of the manga, except what little was translated and released in the states by Viz, and most of that wasn't fabulous. If you can, though, find the "Return of Lum" series, including the chapters about Mendo's introduction, the fake "love letter" to Ataru, and the doll Lum leaves with Ataru when she leaves him. This last one is good in the anime, as well, but the other two might as well be skipped; the manga is better. The introduction of Ran is good as well, both in anime and manga.