I can't imagine memorizing kanji readings on purpose. It's one thing if each kanji had only one reading. But many of them don't. And the ones that don't are usually the most common ones. The thing is, human memory works great when you need to memorize a 1 to 1 association. If A, then B. If 大 then dai. But this then there's 大きい, then there's 大切. These are very common words. However, memorizing a list of things for a single prompt is extremely inefficient. Your memory will rebel and results won't be satisfying at all.
There are even worse examples. One of the most common kanji, 日. What's the reading? Well, when it's by itself, it's "hi". So far so good. Then you see 日本. OK, maybe it can be "ni". Let's swap these two kanji and get 本日. What's the reading now? Umm, it's "jitsu". Three readings, wow. But wait, there's more. Take 一日. The reading is "nichi". And then there's 日曜日, two occurrences of this kanji in one word. The first is read "nichi" again, but the second time it occurs it's "bi". Five readings, all from extremely common words. Are we done? Not quite. 十日 (reading "ka"), 日課 (reading "nitsu"). What about 今日 (kyou)? What about 明日 (asu, ashita), 明後日 (asatte), 昨日 (kinou)? What's the reading now? Oops, there's none, these are a type of ateji (当て字) where kanji were assigned to a word to fit the meaning, with no regard for their pronunciation. Well, you can also read 明日 as myounichi, and 昨日 as sakujitsu, and then you get the old "nichi" and "jitsu" readings. But are you sure you want to memorize all these readings, and then miss out on the ateji exceptions? This just a single kanji. There are over 2000 you NEED to memorize (but better 3000).
You don't even know in advance which readings of a kanji are common and which are not. And memorizing a list of readings is very error prone and frustrating. So what's the solution? To me, it was pretty simple: don't memorize kanji readings, period. Memorize vocab. Instead of memorizing 日 -> hi, ni, nichi, jitsu, ka, memorize 日->hi (day), 日本->nihon, nippon (Japan), 本日->honjitsu (today), 一日->ichinichi (one day), 日曜日->nichiyoubi (Sunday), 今日->kyou (today), 明日->ashita, asu (tomorrow), 十日->tooka (10th of the month) etc. This way you learn a) a whole bunch of useful words, and not just readings that are useless by themselves; b) all common readings of the kanji you're studying; c) all common exceptions such as ateji; d) some readings for a bunch of other kanji that occur with the one you're studying. Overall, it's a lot more fun and efficient if you goal is to master all of them.
Now, where to get vocab for your list is a separate discussion, but the short answer is, use Anki and download Core 2000 and Core 6000 lists that were ripped from smart.fm. Not the best order of words, but these lists are free and in the end they work just fine. Memorize the words, and kanji readings will come to you without you even noticing.