If you do not get the major scale and it relative minor it will be hard to get the other modes.
Playing the major scale using the most simple triads may be the best thing a person can do.
I also would choose arpeggios over modes for a beginner.
Pentatonic Major: 1, 2, 3, 5, 6
Ionian: 1, 2, 3, 4, 5, 6, 7
Lydian: 1, 2, 3, #4, 5, 6, 7
Mixolydian: 1, 2, 3, 4, 5, 6, b7
Pentatonic Minor: 1, b3, 4, 5, b7
Aeolian: 1, 2, b3, 4, 5, b6, b7
Dorian: 1, 2, b3, 4, 5, 6, b7
Phrygian: 1, b2, b3, 4, 5, 6, b7
Yeah poor old Locrian if you playing Diminished chords you are using this, it is just part of the Family.
Peace