For breed and open shows, I always had my mare in a running braid. She is an Arabian though, so the running braid is what is common and expected for her breed. If you are showing a breed that normally has a pulled mane and button or other style braids, you may want to consider showing your horse in their breed's traditional style.
I couldn't find much about showing Standies, but I did find this PDF from the SPPHA (Standardbred Pleasure & Performance Horse Association) This is what they had to say:
"Standardbreds in ridden classes must have manes plaited and tails
plaited, pulled or shaved.
Standardbreds in led classes may have:
a) manes and tails presented as for ridden classes OR
b) bridle path plait – a small section of mane at the top of the
neck is plaited. A discreet colour-coordinated ribbon may be
incorporated into the plait. Tail is left unplaited. (Led
Standardbred ONLY) OR
c) both mane and tail unplaited. (Led Standardbred ONLY).
Bridle should be the same colour as the saddle, supple, of good
quality leather. Stitching on noseband and brow band optional.
Coloured brow bands may be worn. It is preferred that a snaffle bit is
used (jointed or straight bar)."