I really couldn't put a "most important kata" classification on any of them, since each one has something to offer.
Just as a few examples (can't list every lesson, else I'd probably violate a max charater limit), I'd use these points when teaching Shotokan Karate:
At the beginner level, there's the Taikyoku series: Have to start somewhere, and to get good stances, fundamentals, and timings, is critical to someone's development. Since all the stances are zen kutsu dachi, and the same hand / same foot rule applies, it's easy to learn, and that students can soon learn how to refine their performance, once the sequences become second nature. This is where they first "get it," for the lack of a better term.
At the intermediate level, there's Heian Shodan (sometimes swapped with Heian / Pinan Nidan in other systems, since it is a bit more difficult to learn): Their first complex kata. This kata makes them aware that they are going to showing a lot of aspects, such as blocking, punching, open hand techniques, kicking, koshino-kaiten, and also because they are no longer strictly adhering to the classical "H" of the Taikyoku series. Also, one's stances are really highlighted by this form, since they are going to have to make sure that their zen kutsu dachi, kiba dachi, and ko-neko dachi are all in order.
It's really a lot for a newly minted intermediate student to digest, and although the other Heian kata teach equally important techniques and lessons, their first Pinan is going to be a good sized leap, but invariably, they're going do do just fine.
At the advanced level, there's Kanku Dai: A culmination of everything they've learned, plus a bit more. This is where they learn whether or not their endurance is sufficient to go through the whole kata with full intensity, while not fading away. It is, after all, a rather long form. At the same time, though, learning it really isn't that difficult at this stage, since the students can now see (or had better be able to see) that the first half is almost like piecing parts of Heian Shodan and Heian Yondan together, so the familiarity of the techniques is already present.
As a result, they'd better darn well see that the more basic items they learned are going to be with them for the rest of their times as martial artists!
