If you're to be what one would consider a "good" musician, all three things - ear training, finger positions, and the ability to read sheet music - are necessary to learn. Keep in mind that I'll be simplifying some points (almost grossly) to illustrate my main point as simply as I can.
Ear training and memorizing finger positions often go hand in hand, and this combination will become quite important as time goes on. Currently, I'm at the point where if I'm playing something I've never tried to play before, I can get most of the notes right just because I know where the next notes should be in relation to the previous notes I played. I'm good at recognizing intervals (the the audible "distance" between notes) as a result of training my ear, and I can best calculate which fingering should come next as a result of having familiarized myself with finger positions in relation to said intervals.
In short, as long as I know what key a song is in - which, again, is something that is gained by ear training - I can pretty much play something I've never played before with some 70-something percent accuracy, as long as I've listened to the song at least a few times. So both ear training and finger positions are both immensely important, and I urge you to start trying to master those first.
Sheet music, on the other hand, is a whole different animal. Whereas memorizing finger positions has to do with muscle memory (tactile) and ear training has to do with recognizing the quality of intervals (auditory), the ability to read sheet music associates both those qualities with what you see on paper (visual). If I'm to be honest...really, looking at notes on a staff and interpreting them as C, E, G, etc. is no more difficult than than looking at the Cyrillic letters в о д а and interpreting them as v o d a, then further interpreting its meaning to be "water".
...Actually, that really is a great analogy, now that I think about it. Music really is like a language in and of itself; finger positions would be like actually speaking the language, familiarity with interval qualities would be like hearing and understanding the language, and being able to read/write sheet music would be like reading/writing the language in its designated script. And of course you know that most people start out speaking and understanding their language before they learn how to read or write, which is why reading/writing sheet music should come last.
As for exercises on how exactly to work on these things, well...there really is no one way, but among the most common are these:
-To familiarize yourself with fingerings, practice scales. Pretty simple. Major and minor work just fine, but you might want to memorize positions for Dorian, Lydian and the rest of the modes as well, just to be dynamic. Play these scales up, down, over one octave, two octaves, three octaves...etc.
-To train your ear to recognize intervals (quality of 2 notes) and chords (3 or more notes), have one of your siblings or someone else play random intervals or chords (provided they're not exotic chords) for you, and try to guess the quality.
-Then, combine the above two exercises by observing intervals in relation to the fingerings themselves. For example, you'll eventually learn that hitting two keys right next to each other produces a minor second, etc.
-Before trying to master reading sheet music, I suggest you get a good grasp on the other three exercises first. First thing to learn are the notes for each clef...mnemonics really help here (e.g., for treble clef: Every Good Boy Does Fine for the lines of the staff, FACE for the spaces between; for bass clef, Good Burritos Don't Fall Apart on the lines, All Cars Eat Gas for the spaces). After you've got a good grasp of that, print out some blank manuscript paper and plot down some random notes, then sit down and try to play them.
I know I'm usually pretty poor at explaining things, but I hope this wall of text has helped you in some way.
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