Basically there are two kinds of kanji readings; kunyomi (Japanese reading) and onyomi (Chinese reading). However, to our demise, it's not like each kanji only has two readings. Some have only one reading; some have one for on and one for kun; some have more than once for on and kun each. There are also kanji that have hiragana following them, mostly kanji for verbs and some adjectives; rarely nouns. The hiragana following such kanji is called okurigana.
Usually, kun reading is used when the kanji stands alone or when used with okurigana. When it's combined with other kanji,
usually the on reading is used.
For example,
姉 has a kun reading of "ane" and an on reading of "shi".
妹 has a kun reading of "imouto" and an on reading of "mai".
When combined, I wouldn't say you can't read them as "ane imouto"; but as a proper word, 姉妹 is read as "shimai".
About the kanji commonly used in visual novels, eh... I find it a hard question to answer. No, actually, I should say that I can't answer it, to be honest. First of all, even visual novels, being the hardest compared to animu and mango, differ in language difficulty level among themselves. You may be able to get the gist of an everyday school romance VN by knowing basic conversations, but for things like Chaos;Head and Steins;Gate...
Therefore~ my advice would be: study and memorise kanji by the order of Jouyou grade or JLPT level. If you neither have a text book nor are you taking a course, you can use some utility software and sites, like
zKanji - it has an option to list kanji by Jouyou grade or JLPT level, so it'll be easier and neater for you to learn.