Could it be you’re specifically confused about the kun’yomi and on’yomi of numbers? Think you’re getting confused about counter words rather than readings. When you count things in Japanese, you have to use a counter word. English has a few, but they’re not as ubiquitous – for example “ten head of cattle”, “sixteen pairs of pants”, “ninety-nine bottles of beer”.

What you’re talking about is やっつ. The つ counter is a special one that uses the kun’yomi for the numbers one to ten. (It does, supposedly, continue past ten, but it’s essentially never used.) It’s essentially used to count generic “things”. “Eight of those, please” sort of thing.

To count non-generic things, you need to use a specific counter word, and (aside from 一人, 二人 and the weird freaky readings that go with 日) all of the specific counters use on’yomi… so far as I can recall. For example, dogs and cats use 匹 (ひき). Eight of them would be 八匹 (はっぴき – yes, some of the numbers do weird things to the counters’ readings).

Wikipedia’s article on this subject is pretty good: http://en.wikipedia.org/wiki/Japanese_counter_word

So, back in the depths of pre-history, Japan already had its own spoken language, but no written language (that’s what makes it pre-history, you see). They had their own words for things like trees, rocks, people, et cetera. When Buddhist scholars arrived from China, they brough with them the Chinese writing system, as well as words for more esoteric concepts like government, taxation, humankind, and so forth. This imported writing system was applied to the existing Japanese spoken language, becoming kanji (and later, hiragana, and even later on, katakana).

Which brings us to on’yomi and kun’yomi. The kun’yomi are the native readings that were given to the kanji when they were brought over to Japan, while the on’yomi are the Chinese readings that were imported along with the kanji. Some kanji have no kun’yomi, and interestingly enough, there’s even a handful of kanji with no on’yomi.

Typically, you’ll use the kun’yomi when a character is standing on its own (for example, 話 on its own is read as はなし) or with okurigana, hiragana tacked on the ends of verbs and adjectives to indicate conjugation and whatnot (for example, 話 as part of 話す is read as はな – this will typically be written in kanji dictionaries as something like はな・す or はな(す) to indicate which bit is the kanji’s reading and which bit is okurigana). You’ll use the on’yomi when a character is in a compound word along with other kanji (for example, 話 in 電話 is read as わ).

This is not a hard-and-fast rule – there’s about a thousand and one exceptions – but once you start to get a lot of vocab under your belt, you’ll start to get a feel for which reading goes where. I can generally intuit the reading of a word I’ve never seen before, if I know the kanji (and sometimes I can even intuit the readings of kanji I’ve never seen before). I kinda think the more nature-oriented a word is, the more likely it is to use kun’yomi (for example, 川口, river mouth, uses the kun’yomi for both characters: かわぐち).

My suggestion is not to try to learn the readings in isolation – learn vocab, and the readings should come to you as a result.