Traditionally, the modes didn't transpose (we're talking medieval music) so music theory has been hugely in the total series. Further, modes are kind of limited to 7 scales, all built around the Major scale pattern (Ionian, for purists). Tonal music uses more Baroque, Classical, and Romantic concepts of the major and minor scales. And it's quite arguable that other than the very liberal 20th century composers, most of the popular music on the radio waves are descendents of the tonal series.
And yeah, piano's the way to go for a general sense, though I've been learning theory the way a person working with a fretboard (guitar, mandolin, etc) learns, and it's quite a different take on the rules I know already from my piano theory.
Also, from personal teaching, I have students that don't play piano, but rather just a string instrument or even a wind. They need to have supplementary knowledge, such as techniques (string has up-bow vs down-bow, pizzicato, etc.) or a viola student will need to work with the alto/viola clef. I have a couple students that know how to read treble, bass, and viola clef, and they're on the beginning book. Rather impressive compared to others that learn just treble and bass and they're in the advanced levels.
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