To be totally honest with you I fully believe that learning individual kanji is 100% useless and a waste of time.
I've only taken two semesters of college level Japanese, but from my experience you would save yourself tons of stress and time if you just focused on learning the words that kanji are used in. So for example, I would never try to just learn 暖 by itself, because you will never see that kanji by itself anywhere except in a textbook. Instead, I would learn the word 暖かい, what it means, how it's pronounced, and of course how to write the kanji within it.
As for learning to write the kanji, I've just gotten to the point of breaking it into smaller pieces and learning to write those small pieces quickly and easily. Not necessarily focusing on radicals on purpose, like their meanings or anything, but just what they look like. For example, in the example above, 暖, just by glancing at it, I can see it has the shapes of the kanjis 日 and 友 built into it. Since I can already draw those two kanji easily, then I know I can draw this one pretty easily as well. Learning how to write new kanji builds upon itself and once you becoming familiar with more and more shapes, you find it easier to write new ones you learn. Soon you won't have to go stroke by stroke anymore. Instead you can see more complex kanji as just a combination of a few kanji that you already know.
Learning vocabulary (in context!!!) is a hundred times better than learning a kanji on its own, because it actually adds something useful to your Japanese language bank. Now, instead of knowing some random symbol, an abstract discription of it, and a couple of *possible* pronunciations, you'll know an actual word that you can actually use in a sentence. For context, I use manga. I read manga that has furigana so I can easily look new words up the a dictionary app I have on my phone, then I save the new words into the built in flashcard part of the app and study it until I know it (if you have an iPhone the app is simply called "Japanese" and it is AMAZING! it's $8 but worth every single penny & this is from someone who NEVER used to pay for apps!). After learning the meaning of the words (focusing on the definition that fits with the context I found it in) I go back and reread the manga, further solidifying my knowledge of the words and of course giving myself a REASON to remember it. Context helps things stick 100x better. The app also has an animation of how to write the word's kanji stroke by stroke if you need that too.
I've only read a little of the Genki 1 textbook (it's different than the one we used in my college classes) so I haven't yet gotten to the Kanji part. But if it's anything like the one I used, it's probably set up to where you learn each individual kanji and there will be a few examples of how it's used. If I were you, I'd learn the stroke order just to learn how to properly write these beginning kanji, then focus on the WORDS. Don't try to learn the onyomi or kunyomi by itself. Go ahead and glance at the "meaning" of the individual kanji (for example, in the dictionary in my phone, 暖 means "warmth") but DON'T try to memorize it. Just go for the actual WORDS, the meanings of those WORDS, and how the kanji is pronounced in those WORDS (so learn that 暖かい is pronounced "あたたかい", and that it means warm or genial and is used to describe weather.)