As an owner of two Standardbreds, and a show groom for one of my friends who heavily shows her SBs, I can help!
What kind of show is it? If you're allowed to plait (make sure it's not in the rules saying "no plaiting").. I would just do traditional plaiting, of the tail and mane. Turnout for a SB is like turnout for any other horse, neat, presentable, and clean.
Showing standardbreds is like showing any other horse... depending on what you're doing (inhand or ridden), as long as you keep your horse moving active on your aids, you should be fine.
Are you showing in a SB ring or another?
All the best.
♥ Seoul Searchin' for the Lovebug ♥