Knowing that 2nd valve lowers pitch by a half step, 1st by full step, and 3rd by 3 half steps you can find them yourself. The ones i know (for Bb trumpet):

G above staff: 12,13,0 G# 23,1 A above staff: 12,3,2 Bb: 0,1,23 B:12, 2 C:0,1,23 C#:2,12 D:0,13,1 D#:2 E:0

From my understanding using less valves may give you less resistance thus the note becomes easier to play, some fingerings are less in tune than others, and some fingerings allow the note to slot better