What's the most important teaching of the Buddha in the canon?

Didn't Guatamala Buhddalicious suggest being mindfull? ahem mindful? I think that's important (sure hope it's a precept, or in the canon or whatever.)

I grew up when non-(za)Zen type of Buddhism was popular, but I discover "becoming one" with it all right when I needed it the most. Let's just say, it felt like I was having "bad" Karma, but really, it all worked out. For me.

I read books like "Hardcore Zen" by Brad Warner, the "Zen of Juggling" byt Dave Finnegan, & two books by Philip Toshio SUDO, "Zen Computer/Guitar". & alsom started watching Alan Watts' old school colorless movies on public access cable television (somebody got a mindnight timeslot. midnight! ahem)

I've of course studied more since then, but those things helped to spark my consciousness, personally.

I wouldn't worry too much about pressuring anybody into this kind of thing. & yes, exposure to something you have expressed no interest in can sometimes feel like, one is a horse, being lead, to, play a game of horse shoes. U Good luck. ........(five minutes later) I think I was being mindless, and not the good kind (I'm freeing my mind, ok freeing my mind here we go). I forgot I helped make this video, it could spark a person. Actually, it did, the event, & the video. here, take this: https://archive.org/embed/dalai-lama-magic-mouse-stringless-yo-yo-jj-fixed-analog-audio-ver-1.0 i'll go now. be well/safe, party on, good luck. (leaving my typos. they are fine. at least they're not spelling errors, right? & good luck is better x2-JJ)

Saṁyutta Nikāya 3:25 Pabbatopama Sutta: The Simile of the Mountains

transl. Thanissaro (text) https://www.dhammatalks.org/suttas/SN/SN3_25.html

(mp3 audio) https://suttareadings.net/audio/sn03.025.than.mp3

In the Mahasatipatthana sutta, Buddha says the following, at the very start of the sutta and at the end of the sutta-

"This is the one and the only way, monks, for the purification of beings, for the overcoming of sorrow and lamentation, for the extinguishing of suffering and grief, for walking on the path of truth, for the realization of Nibbana: that is the fourfold establishing of awareness."

In the light of Buddha asserting it to be the one and the only way, I think it can be said to be the most important teaching of the Buddha; though the teaching on Four Noble Truths in Dhammacakkapavattana sutta may well be put in the same category.

To spark an interest i would go with the Itivuttaka collection. My introduction was with Itivuttaka 91.

https://www.dhammatalks.org/suttas/KN/Iti/iti91.html

OP: What's the most important teaching of the Buddha in the canon?

I would say the most important teaching of the Buddha, for a very advanced person, would be the Bahiya Sutta, which is already referenced in Max's answer. The Buddha could only teach one thing to Bahiya and he taught this teaching about anatta:

"Herein, Bahiya, you should train yourself thus: 'In the seen will be merely what is seen; in the heard will be merely what is heard; in the sensed will be merely what is sensed; in the cognized will be merely what is cognized.' In this way you should train yourself, Bahiya.

"When, Bahiya, for you in the seen is merely what is seen... in the cognized is merely what is cognized, then, Bahiya, you will not be 'with that.' When, Bahiya, you are not 'with that,' then, Bahiya, you will not be 'in that.' When, Bahiya, you are not 'in that,' then, Bahiya, you will be neither here nor beyond nor in between the two. Just this is the end of suffering."
Bahiya Sutta (Ud 1.10)

OP: Or, what would be the best teaching to spark an interest in someone who knows little or nothing about the teachings of the Buddha?

Now this is a totally different question from the first one.

To a complete beginner, who is usually also a lay person, who has never heard of any teachings from the Buddha, the following opening verses of the Dhammapada would be interesting:

1. Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with an impure mind a person speaks or acts suffering follows him like the wheel that follows the foot of the ox.

2. Mind precedes all mental states. Mind is their chief; they are all mind-wrought. If with a pure mind a person speaks or acts happiness follows him like his never-departing shadow.

3. "He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.

4. "He abused me, he struck me, he overpowered me, he robbed me." Those who do not harbor such thoughts still their hatred.

5. Hatred is never appeased by hatred in this world. By non-hatred alone is hatred appeased. This is a law eternal.

6. There are those who do not realize that one day we all must die. But those who do realize this settle their quarrels.
   Dhammapada chapter 1

And also the golden rule:

Searching all directions
with your awareness,
you find no one dearer
than yourself.
In the same way, others
are thickly dear to themselves.
So you shouldn't hurt others
if you love yourself.
Ud 5.1

For me the most important teaching is the noble truths, i.e. understanding sorrow and its ending.

Doctrines like anatta follow from that and so I'd call them secondary (and yet instrumental and non-obvious).

Beyond just "me" are social doctrines e.g. about sila and the brahma-viharas.

Two other aspects of the teaching that I consider important and remarkable, which distinguish it, are:

• Dhammānusati

  The Dhamma is well declared by the Bhagavā: visible here and now, immediate, inviting to come and see, effective, to be individually ascertained by the wise.
  Svākkhāto bhagavatā dhammo: sandiṭṭhiko akāliko ehipassiko opaneyyiko paccattaṃ veditabbo viññūhī ti.

  This is different from the argument proposed in some theistic religions, i.e. "Do not sin, because sin is against God's will, and for sin you are punished on Judgement Day" -- i.e. a hypothetical future and arbitrary rules, which you may not believe in

• The idea that "the Noble Sangha" and "the wise" might assess whether something is "Right" -- I find that more concrete than the idea that there's a God who judges (there may be analogs in a theistic religion, e.g. Saints and Church, but even so).

Having read a lot about Buddhism and practiced meditation, I once told a monk-to-be that I felt really inspired by Buddhism. So he asked me, "What are the Four Noble Truths?" And I could not answer. That shocked moment of silent perplexity sparked a newfound interest and a conviction to learn. It was the first true step.

SN56.27:1.1: “Mendicants, there are these four noble truths.
SN56.27:1.2: What four?
SN56.27:1.3: The noble truths of suffering, the origin of suffering, the cessation of suffering, and the practice that leads to the cessation of suffering.
SN56.27:1.4: These four noble truths are real, not unreal, not otherwise.
SN56.27:1.5: That’s why they’re called ‘noble truths’.
SN56.27:2.1: That’s why you should practice meditation …”

I was speaking to a group of people recently, and I noticed something very interesting: each person was being spoken to from a very different place. You see, the perspective of the response changes depending upon who you're speaking to. This comes about from knowing the entire geographical terrain of your own mind, its weather phenomena and its solar cycles. One knows them with such intimacy and detail that one cannot trip on the peaks and troughs, bend from the wind, nor be darkened by the solar storms.

From this 'place', which we might call situational awareness, one can then respond to other minds in accordance to the particular region they may be. The response appears to draw upon the experiential knowledge obtained by 'the journey that led to nowhere' alongside an intuitive awareness of the person and the particular nature of their inquiry.

Listening to another person is very fascinating, indeed. The entire body listens and the mind plays a very minimal role in the process, if barely any. It's even possible to 'listen' to random members of the public in this way, which might reveal some interesting things. It certainly makes a for rich experience when walking through the shopping center!

The Buddha had the same approach where everyone was responded to personally from their perspective taking into account their temperament: that manner of acting, speaking, feeling and doing – basically the formation of the unique set of sankharas that swing their minds hither and yon; that is what he spoke to.

He spoke to that particular potential (sankhara) in those particular people, or even groups, respectively so: with Bahiya, he gave the in the seen, there is just the seen teaching; in the background to the satipathanna sutta, it's said that the Buddha spent some time carefully observing the Kuru people, before concluding that their wisdom was far beyond most other groups of people. From this observation spawned the satipatthana teaching, which is widely renowned in Buddhist circles, if not seen as the most important teaching.

All in all, what initially seems to spark the attention of many people is the idea of compassion, love, kindness, and attentiveness. After all, beneath the incessant urgency and commotion drummed-up by society, these things we all have in common. Peace in the heart is what everyone wants, whether they know it or not. When it has been found in yourself, it will spread in the most amazing and unusual ways!

Note: I prefer Mahayana's conception of compassion, which is generally framed in terms of virtue and is something tangible for the practitioner to hold. Having said that, compassion as a virtue in its finality makes no sense – all moral schemes erode. Something of compassionate acts are performed, but without a structural framework and/or seemingly at the confusion of the worldly ego minds. One cannot understand why a realized one does what they do, for their wisdom eye is wider than the universe itself.