I've tried both this site and anki. While I do kinda like the Leitner system, I prefer automated SRS. There's less overhead on my part. It's not that this system isn't complex or efficient enough, it's just I'm focusing partly more on when to review kanji and stuff as opposed to the kanji themselves.
Anki won't necessarily make the reviews anymore enjoyable, though. That's just the nature of the beast. You'll have to find creative ways like Anki Emperor or Lazy Kanji Mod V2 (I highly recommend this). Lazy Kanji Mod V2 already has stories for every kanji (presumably mainly from this site and perhaps from a few other sources). Obviously if the story sucks or you don't like it, you make your own up, but I find I'm only doing that 1 in every 35 kanji or so.
Also, you can decide what primitives you wish to prioritize. For instance, (lesson 20, kanji #2) kanji frame 510 is burn, which is "fire" on the left and "sort of thing" on the right. If you are shaky on "sort of thing", you can simplify it down into "crescent moon", "chihuahua/dog", and "oven fire (or whatever you call this one)". I mean, if you already knew this tip, sorry, but if you didn't, I think it can help you be more flexible in remembering kanji that are like that.
By the way, are you just starting a general 101 class in high school? Or do you mean you're starting private lessons -during- high school? Because if you're just taking Japanese for the first time, knowing the kana and knowing that many kanji, plus knowing all those phrases, will easily carry you through at least a semester with no effort on your part. You might just learn some readings and very general kana words.
Or are you in, say, Australia, where you've already been studying Japanese for a while? If that's the case, I still wouldn't worry. Classes are pretty easy and any work you're doing outside of class probably won't apply heavily in-class, since they usually kinda suck and sorta focus on grammar and rudimentary language elements (or rote kanji memorization).
