| Major chords are the beginning. You also have minor, diminished, augmented , major 7th, dominant 7th, minor 7th, half diminished, and diminished 7. Sus chords usually refer to the sus 4 but there of course are other sus chords. In the context you are playing, don't go too crazy trying to play chord extensions if you see any such as 9,11, and 13. Although you probably won't see them in the kind of music you are playing. You would really also only be playing the sus 4 of a chord for a certain effect. The band or ensemble would prefer you play the root to the sus 4 of the chord played by the harmonic instrument has an effect.
For example, if the bass does not play the D on a D sus chord, the G does not give the suspended sound against the root. There isn't too much detail to get into to play over such chords. (mixolydian mode for diatonic passing tones and chromatic passing tones if you're going crazy). If you want more info on playiong over chords with tensions such as b9, 9, #9, 11, #11, b13, 13 etc... my book The Total Jazz Bassist digs into that sort of info.
Best,
Dave | 
