I wouldn't bother specifically trying to memorize all the readings of a kanji and when to use them. Many kanji have readings that are only used very rarely, but as a beginner it's difficult to distinguish which readings are common and which ones are not. It saves a lot of time, and frankly is a lot easier, to learn how kanji are read through immersion and absorption. For example, if you see the word 食事(しょくじ), and then the word 食堂(しょくどう), you'll learn to associate the しょく reading with 食 when you see it in compounds.
As for choosing words to learn, I usually don't go actively searching for words to memorize as I don't know if I'll ever need them, but instead learn words that I encounter when reading or watching something. I put words in Anki, a spaced repetition flashcard program, in order to organize and remember them.
March 28, 2016 at 6:06am