Some readings are not common, as well - and even if you can remember a list of them, you still wouldn't know which is read where, some common words are exceptions (like 今日/明日/昨日), so memorising the readings wouldn't help you at all there.
Basically, you just need to increase your vocabulary. As you do, you'll find it easier to guess words - i.e. if you've learnt 部長 and 学校, then both the reading and meaning of 校長 come much easier.
There are some that only have one reading, so in that case, sure, remember that (I believe 駅 is one of them, unless there are some special readings I don't know, and 液 might be another).