It seems like you understand what the various modes so I’ll touch on another aspect of modes; colour. Each mode is associated with a specific type of chord. We’ll use C major just to make it easy to understand.
C Lydian: C D E F# G A B (major mode)
C Ionian: C D E F G A B (major mode since we can clearly see the CEG from C major in it).
C Mixolydian: C D E F G A Bb (major mode)
C Dorian: C D Eb F G A Bb (minor mode since we can see CEbG which makes up C minor).
C Aeolian: C D Eb F G Ab Bb (minor mode)
C Phrygian: C Db Eb F G Ab Bb (minor mode)
C Locrian: C Db Eb F Gb Ab Bb (diminished mode)
This is the order of modes from brightest to darkest. The Lydian mode is has the signature #4, which makes it very bright. Each mode has a signature tone that makes it unique. Note, we can also extend each mode to be used with 7th chords.
C Lydian - C major 7
C Ionian - C major 7
C Mixolydian - C7
C Dorian - Cm7
C Aeolian - Cm7
C Phrygian - Cm7
C Locrian - Cm7b5 a.k.a C half-diminished
Modes & Chord Progressions
Let’s take a look at using modes in the context of a chord progression. Modes/scales go together with chords, which means that the notes of the scale or mode are found in the current chord that we’re playing. Our chord progression will be in the key of C and is as follows:
Since the first chord is major, we can use any of the major modes to solo over top of it: C Lydian or C Ionian. Note, using C Ionian will simply keep all of the notes in the scale of C major, but C Lydian will sound a bit more exotic due to the #4. Chord 2 is A minor, which means we’ll use any of the minor modes: A Dorian, A Phrygian or A Aeolian. Of course, A Aeolian is simply all of the notes from the scale of C major. I’ll skip chord 3, since it’s the same as chord 2, but with D as the root. Chord 4 is G7, which is a dominant 7th chord. For this chord, we’ll use the Mixolydian mode, which would be G Mixolydian. Please note, this is a simplistic view for using modes and scales with chords.
For instance, the last chord in the example was G7. We can use any scale that contains a G, B, D and F. Here are a few below:
1) Mixolydian: G A B C D E F G
2) Half-Whole Diminished Scale: G Ab A# B C# D E F G (notice how it contains G B D and F)
3) Altered Scale: G Ab A# B C# Eb F G (the 5th, D, is not commonly listed, but it’s a “hidden” tone of the scale)