We have the basic scales; Pentatonic, blues scale, major, minor, whole tone, and chromatic. When we take the major scale and start building on top of each scale degree, we start getting into modes. For example, C major scale. The notes are C,D,E,F,G,A,B,C. If we start with the 2nd degree, D. We have D,E,F,G,A,B,C,D. That is D Dorian. Even though it has the same notes as C major scale, we are starting on D. The Dorian scale is a minor scale. The 3rd Degree is E,F,G,A,B,C,D,E and that is Phrygian. 4th degree is Lydian, 5th degree is Mixolydian, 6th degree is Aeolian and 7th degree is Locrian.
We also have natural minor, melodic minor, and harmonic minor.
Then the next one is whole tone scale and chromatic scale.
We also have hybrid scales, where we use a combination of notes from 2 different modes. For example, we can use Phrygian scale with a #4. E,F,G,A#,B,C,D,E. The #4 is technically from the Lydian scale.
We also have many different alterations of scales from different cultures around the world. For example, a common one is a middle eastern sounding scales, also known as the Egyptian minor scale, I, bII, #3, 4,5, b6, 7. To play a D Egyptian minor scale, the notes are D, Eb, F#, G, A, Bb, C and D.
We also have microtones scales from Arabic world and Raggas from India.
You should know the basic scales and if you are really interested in other forms, you can consider studying them.
The best way to learn the scales is to play and practice your scale exercises. After that you can learn to improvise with the scales by playing a drone rhythm track.
Arpeggios are broken chords. For example, a C chord is C/E/G. If you play all 3 notes at once, it’s a chord. If you play, C, E, G, one at a time. That’s a broken chord or an arpeggio.