Kanji studying misgivings

I continue to have misgivings about my kanji studying methodology. I've bounced around between several different methodologies, and even gave up on studying kanji for a while as I focused again on grammar constructs. I'm still convinced though that my ability to learn the language will greatly increase if I am able to read books, and for that I need to "know" kanji.

First a little background on kanji. Each kanji can have a variety of meanings, but those meanings all relate to each other. I'm going to use "ishi" (石) as my example, since it pretty much means "stone". Now, in Japanese kanji can have several different "readings". While the kanji itself means stone, depending on what word that kanji shows up in, it might sound like seki,shaku, koku, or ishi. The kanji finds itself in such words as oil, stone, pebble, coal, jewel. You can see how those words are all related to stones. My dilemma is that just knowing the meaning of a kanji doesn't necessarily help. When I'm trying to read a word that is composed of two or three kanji, even if I know the meaning of the individual kanji, that doesn't give me how to read the word, or what word the three kanji together form. As I mentioned above, if I see 石, it could be read in one of several different ways. Do I study the kanji, the meaning, and memorize all of the readings? Will those readings help me by themselves? I've used a methodology whereby instead of studying just the readings, I've actually memorized words that the kanji shows up in. In that way it's more like memorizing vocabulary than individual kanji. I automatically know how to read the word since I memorized that group of kanji's reading.

While that is a great way to eventually learn how to read, it also seems very inefficient. I could learn a word for every one of 石's readings (in this case four words). This means that I would put my effort into learning how to write 石, the meaning of 石, four words which contain the different readings of 石, those word's meanings, and how to read those words. Instead of doing all of that, I could just learn how to write 石, the meaning of 石, and the four readings related to it. Is the latter approach the better way of learning kanji? Is it too artificial to be useful for reading? In the latter case, I might know all of the readings for a kanji when I come across it in a word, but I won't necessarily know which reading is correct, or the meaning of the word. I think I will try to switch to the latter method in the hopes that being familiar with a lot more kanji will let me more easily match up words in kanji whose readings I don't know with vocabulary that I memorized without learning the kanji.