Aye, once you’ve got a bunch of kanji and vocab under your belt, you’ll start to get a feel for which reading goes were. You’ll even start to be able to intuit readings of words you’ve never seen before.

大人 is one of them freaky exceptions. It’s おとな (otona). =)

That said, if you were going to guess the reading of a word you’ve never seen before, you’d typically go with the on’yomi when it’s a compound noun made from multiple kanji. In this case, that’d be だいにん (dainin).

Welcome!

Koichi’s explanation on this is a little muddied, but basically the rough rule of thumb is this:

-When a kanji is standing on its own, or has okurigana (hiragana stapled on the back that indicates verb and adjective conjugations), then you use kun’yomi.
-When a kanji is in a compound word with other kanjim you use on’yomi.

Basically, way back in prehistory, Japanese had a spoken language, but no writing system (which is what makes it prehistory). Then Buddhist scholars came to Japan, bringing with them the Chinese writing system. These Chinese characters were used to express words which already existed in Japanese, and these native Japanese words became the kun’yomi. You’ll tend to find that kun’yomi words express basic physical and natural items – trees, rocks, rivers, body parts, verbs, and so on and so forth.

However, the introduced Chinese characters already had Chinese pronunciations – these pronunciations became the on’yomi. The scholars also brought with them more esoteric concepts like government, taxation, and so on and so forth.

So to use an example, the kanji 話 uses its kun’yomi はなす when it’s standing alone. When it’s got an okurigana ending, 話す, it uses a slightly different kun’yomi, はな (you’ll tend to see this written in dictionaries as はな・す or はな（す） to make it clear that はな is the reading of the kanji and す is the okurigana). When in a compound word, say 電話, it uses its on’yomi わ.

There’s about a thousand and one exceptions, though. Rule number one in Japanese: all rules have exceptions, including this one.

I feel like the more concrete and nature-themed a word is, the more likely it is to use kun’yomi, but that’s just my gut feeling, and I’ve got no particular proof of that. Case in point: 川口 (river mouth) uses the kun’yomi for both kanji, despite being a compound word – it’s かわぐち.

Anyway, after all that, like Brook I would advise against trying to learn the readings in isolation. If you just try to go “well that’s kun’yomi and that’s on’yomi” without anything to anchor it to, you’re just going to forget it again. Start learning vocab (with kanji) and you’ll start to get a feel for which reading goes where before too long. You’ll even start to be able to intuit the readings of words you’ve never seen before.

There ARE groupings of verbs, but I don’t know if it’s official or just out of convenience.

… And at the moment, I’ve clean forgotten what they were. State, movement, and… existence? Something something.

Welcome! Welcome!

What are you planning to do in Tokyo, Sam?

Honestly, Koichi kind of muddies the waters a little bit by treating “subject” and “topic” as synonyms, when in a grammatical sense, they’re not. The topic (marked by は) is what the sentence is about, while the subject (marked by が) is the doer of the verb. Often the topic IS the subject, in which case the は replaces the が, but the topic could also be the direct object (in which case the は replaces を), or the location-of-action (where は and で join forces to produce では), and so forth.

A better “translation” for は would be “on the topic of X”, though that produces some rather clunky wording in English.

キリンは首が長いです = on the topic of giraffes, their necks are long
リンゴは果物です = on the topic of apples, apples are fruit (case of the subject being the topic)

I don’t believe treating は as a verb is terribly helpful. That’s very much a case of trying to squeeze Japanese into an English S-V-O format, when Japanese is S-O-V – the verb goes at the end. It’s interesting that you also bring up postpositions, because that’s exactly what particles are in Japanese – all particles modify the word that comes before them (as opposed to English’s reliance on prepositions, which modify the word that comes after).

As for です, it’s called the copula, which is a verb-like object that goes in a sentence where no verb is needed. The copula in English happens to be “to be”, which is why people tend to say です = to be, but note that it’s not a direct translation. です is in a part of speech all on its very own, though slightly confusingly, the more formal literary version is である, which is a verb.

I’m vaguely hoping I’ve addressed your concerns, but it’s late and I’m tired, so I’ve probably missed the point completely. =)