I usually recommend the manga, but this anime was not made off of a manga, and was, in fact, original, actually basing itself on a short movie and redefiining it instead of using a manga as a source.
Princess Tutu = ANIME
Another case of the anime being the original. The manga adaptation takes out everything that makes the story unique, and condenses the entire series into a two-volume rather typical Magical Girl series.
Skip Beat = MANGA
Only because the anime is new, and you'll get much farther by reading the manga.
I can't actually help with the others, though...
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