Here's how I approach it: forget about all the historic naming like "perfect fifths" and just think in terms of the modern 12-note equal temperament. Every note is a number, e.g. 440 Herz = 69, the standard guitar tuning has strings from 40 to 64, etc. Every interval is an integer, up an octave is +12, major chord is a triple of {x, x+4, x+7}, minor seventh chord is {x, x+3, x+7, x+10} etc.
Then, as a the second game-changer, learn the circle of fifths. Start with a note like C, and keep adding +7 to it. You'll get FCGDAEBF#C#G#D#A# - note how the sharped notes repeat the pattern of the nonsharped ones, easy to remember. The "keys" and "modes" stuff is just intervals of seven consecutive notes on the circle. Say you choose FCGDAEB, that's one key, then every mode is to be found by choosing one note out of those seven, and hopping over one note until you play all seven once: e.g. FGABCDE is one mode (Lydian afair), EFGABCD is another one etc. The "major" and "minor" keys are just different names for two of those seven modes. Pentatonic scales are those same modes with some notes omitted. Blues and harmonic minor scales are those same modes with some notes inserted. Overall modes, not keys or chords are the key to actually composing music intelligently, so learn them and learn to play them.
This should give you a good start in practical music theory.
Then, as a the second game-changer, learn the circle of fifths. Start with a note like C, and keep adding +7 to it. You'll get FCGDAEBF#C#G#D#A# - note how the sharped notes repeat the pattern of the nonsharped ones, easy to remember. The "keys" and "modes" stuff is just intervals of seven consecutive notes on the circle. Say you choose FCGDAEB, that's one key, then every mode is to be found by choosing one note out of those seven, and hopping over one note until you play all seven once: e.g. FGABCDE is one mode (Lydian afair), EFGABCD is another one etc. The "major" and "minor" keys are just different names for two of those seven modes. Pentatonic scales are those same modes with some notes omitted. Blues and harmonic minor scales are those same modes with some notes inserted. Overall modes, not keys or chords are the key to actually composing music intelligently, so learn them and learn to play them.
This should give you a good start in practical music theory.