I agree with Mario, do whatever you feel most comfortable with. If you find it meaningless to learn the on/kun readings, then this means that you won't learn it as effectively as if you were doing something that you actually find useful and interesting. As for me, I've never really cared about learning the on/kun readings, I've just focused on increasing my vocabulary, and as my vocabulary increases, I learn more readings for the kanji. がんばって！

Every person learns differently, whatever you enjoy the most, understand the most and makes you feel like you are learning, that is the right way for you to learn. If you try a kind of exercise and you find it too hard, try something else, do not push yourself to do things that are not interesting or fun for you. Interest works as a motivating factor in learning. Mastering a language (being able to express yourself and understand colloquial, professional and literary fields) usually takes over two years, that means that you need to constantly motivate yourself, not torture yourself. I recommend you to try as many things as possible to learn, imitate what other people do to learn, but if you feel that it is not working for you, it does not mean that you are not a good learner, it just means that you learn in a different ways. There are tons of ways of learning a language, there is no point on doing things that are boring for you, you can find interesting or fun ways to learn all the time... whatever you do, keep on learning. You will eventually master it.

I think, words are more important. Focusing on readings without memorising words is useless. There are many readings which aren't important for beginners to learn, and there are irregular kanji readings. In fact, when you memorise words with their kanji, you memorise readings as well, but not all readings. For example, when you memorise the word 大学 that means you know the reading of 大 and 学, then when you memorise 学ぶ you know another reading for 学, and so on. So, it's better to learn new words with their kanji.

What I have my students do is both in parallel: we study kanji in the order they appear in grade school in Japan, but I make sure they learn at least one word for each reading AND I use one of those words for each kanji in their next quiz. Ex: 本 ＝　ホン、もと　日本（にほん）、本橋（もとはし） 本橋さんが日本にすんでいます。 This way students see how the kanji are used, see which environments trigger on-yomi or kun-yomi, and learn new words/names in the process. Once you get to a certain point I recommend you just start reading and when you come across a kanji you don't know, look it up. You'll learn the kanji and the word at the same time that way. I guess what I'm saying is learning kanji and learning vocab really go hand in hand.

I totally agree with Mario, and with other people, too. If you memorized all of Hiragana and Katakana, you can communicate without kanji though knowing kanji helps you with communicate more easily. We, the Japanese people, study kanji in scholl from 6-year old until 15-year old (or 18-year old), there are more kanji and we all don't know all of them. Plus I forgot a lot after using cell phone and PC however I know how to read them. Please do not think too much about the number "2000", it's better to learn them little by little. Good luck to you.