Personally, I find in easier to just focus on the elements of the kanji that make them sound the way they do. As far as on'yomi go, there are a lot of regular elements that are used to give them the kanji their phonetic properties.
i definitely agree.
Though when I learned kanji, I didn't actively try to learn them that way, it just kind of happpened. The same with radicals. And I think coming to that realization on my own was an asset for learning kanji. Up until last year I hadn't opened a japanese book in about 5 years. Yet, most of the kanji knowledge was still there... so I must have done something right.
My Japanese classes were all very weak in kanji, so I studied them a lot independently.
And I think that the key to my successful kanji learning was simply writing them over and over and over. whenever i had 5 minutes to spare. in h.s. it was easy to look like i was paying attention in one class, while practicing japanese in another.
Beyond what's taught in your Japanese textbook (and if you're not using some sort of text, you really should consider it. it gives your studies a framework. and it's motivational to work from beginning to end of something).... Learning kanji in context - I would learn the kanji that related to other subjects i was studying, and add those into my notes (if i was indeed paying attention to that classes lecture) Start learning the words on the memos that you get at work, or whatever papers you have on your desk.
Everyone has a different learning style, and it will take time to learn what's right for you. And don't forget that Japanese kids spend about 9 years learning all of the 2000 joyo kanji.