You mention being a fan of video game music, so maybe try to find classical music that's similar to the game music you like. That way, it's more a matter of branching out from what you know. That's how I started out listening to classical music. For example, I'm certain that Masashi Hamauzu drew inspiration from Prokofiev in his soundtrack for Final Fantasy XIII:
As for choral music... I can't help you much there. It can be pretty dull. Though, some things I've paid attention to at choral concerts are how in-tune the singers are rhythmically and tonally. And watching how they react to the conductor. In choral music, you'll notice that the conductor doesn't just beat time. They also manage the synchronization of word-shaping. For example, through hand gestures, they try to synchronize the pronunciation of consonants like "k" so that all the singers generate the sound at the same time. Otherwise, the lyrics and rhythms will sound smeared.
And if you're into audio production and mixing, pay attention to how deeper and higher voices balance and reverberate in the particular setting. The human voice is pretty complex, so making a choir sound coherent in a large, reverberant space is actually quite a feat in real-time, acoustic mixing!