Quote:
Originally Posted by YuriTokoro
Yes.
You need to memorize both on and kun. If you don’t, you can’t read Japanese sentences.
Good luck! 
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This is correct. However, OP should know it's not going to be productive to sit down and just memorize the readings for each kanji alone. Instead, it works better, to learn a ton of words that use the ON and KUN readings. (I know you know this already, Yuri, seeing how it's probably how you learned the kanji as a kid!)
For example, OP could either learn 学:学(ぶ)、ガク or he could learn 学ぶ (to learn), 数学(すうがく) (mathematics), 科学(かがく)(chemistry), 物理学(ぶつりがく) (biology), 学期(がっき) (semester), etc.
The first looks easier at first, but it becomes harder after a while. By learning vocab instead, you are able to often learn one kanji's reading while reinforcing your knowledge of another kanji's reading.
For example, if I learn all those words above, I will have a bigger vocabulary and I will also partially learn 数 is すう, 科 is か, 物 is ぶつ, 理 is り, etc. Then when it comes time to learn 生物, I may already recognize ぶつ, so I just need to learn 生 (せい、じょう、なま、etc.)
I've tried both routes. After about 100–200 kanji at 20 per week, method 1 (just learn the kanji) got pretty hard. However, It wasn't until around 800–1000 kanji at 100/week with method 2 that things became hard. (Keep in mind I am not a newbie, though, so my rate of learning would be higher than yours, OP.)
The effectiveness of method 2 is precisely why I champion Anki and Kanji in Context. I've grown my vocabulary by 5000 words and can read so much more at will than I could in, say, March 2010.