Ear Training/Music Theory
Ear training is a useful, often crucial, part of learning how to sing. Ear training enables you to hear a note in your head before you sing it, to know you are singing the right note, it enables you to harmonize, improvise, read sheet music, and more!
Learning an Instrument (Especially Piano!)
Learning an instrument almost always benefits a singer in some way, but piano is very, very, useful. To be just proficient at piano develops your ear, improves your singing, an gives you a tangible way to check your notes and learn a song. Of course, learning the piano gives you an overall idea of how music works in general in a nice, logical format.
Acting regularly has profound influences on singers, because they help expressiveness become central in singing, which is the whole point of vocal technique anyway: to express a message. Singers often get pulled into sound rather than visual communication, and acting not only makes the message front and center, but also helps trigger more genuine emotional expressiveness by cueing facial and body movements on singing, something that many singers forget to use. This often leads to new sounds! A great and sometimes huge side benefit!
The reward of learning vocal technique is not just in new sound possibilities, it’s in new ways to play! Singers in the right circumstances find that having fun experimenting with how they express a phrase, note, tone, volume, consonant, tempo, etc. leads to more individuality and/or proficiency as a singer.
Listening deeply to a genre helps you develop your own style within a genre. You can’t sing opera if you’ve never heard it, and you certainly can’t make a name of yourself within the world of opera if you don’t know the sound parameters that make the operatic sound.
What if you know a genre well but are yearning to break convention?
Well luckily, legend wasn’t made by only singers who were well-behaved. Learn multiple genres deeply, and then break all the rules. In the process, you’ll find your sound.