[Nagoyankee]

Here's how we Japanese learn kanji.

After having mastered both hiragana and katakana (in that order, ALWAYS) in the first few months of Grade One, kids start learning kanji. They learn kanji in the order that they appear in their Japanese textbook. I want to stress here that they don't learn kanji randomly but do so in context. They naturally start with the easiest ones like 山、川、一、二、三、etc.. And the kanji readings that the kids learn at this stage is almsot strictly 'kun'. In the mind of a Japanese native speaker, the 'kun' reading is THE main reading. The 'on' reading basically came from another country as you know.

The terms 'on' and 'kun' may be explained during Grade One, but many kids simply will not understand what they mean because they don't know enough kanji yet. If there's the sentence 「あの山はたかいねぇ」 in the textbook, then the kids learn the kanji 山 (yama). At this time, the teacher may not explain that the kanji can also be read as 'san'. This is because that kanji isn't often read for its 'on' reading in the vocabulary of many first-graders.

As the kids progress, however, they will start learning kanji compounds. We're now talking about the end of first grade or the beginning of second grade. Only at this time, the teacher has to make sure that the kids　understand the difference between the 'on' and 'kun' readings of kanji. I'm sure that you know this is because in compounds more kanji are read for their 'on' readings. This is the time when Japanese kids face a MAJOR problem in learning reading/writing. A kid finds out that the kanji that he always thought was read 'yama' is now being read 'san'. There's no phonetic similarity whatsoever between those two readings!

Extremely strict teachers might try to teach the kids all the possible readings at once. But the great majority of the kids will have a hard time memorizing them. So most teachers and parents are willing to give the kids enough time to learn all the readings, specifically until the kids learn the compounds where they have to know the readings used in them.

You asked about compounds like 失礼, if a particular school uses a textbook in which the word appears first as a compound, then the kid will learn it as one unit. But even in that case, the meaning and the on and kun readings of each kanji will be taught. The chances are, however, a kid will learn the first kanji in the verb 'to lose' and the second kanji in the noun 'thanks' before he encounters the compound. There are no definate rules as to kanji first or compounds first.

I hope this helps but I really need a few more pages to fully explain this.