I have been asked to show my friends appaloosa yearling colt and her welsh part bred 11yr gelding in hand. I am unsure what tack and clothing are used as I only normally do ridden showing of a sports horse
When I showed on the line, it was absolutely necessary to braid (hunter braids - no big dressage braids). A bridle with a regular snaffle bit and a crop is really all that is needed. To get my horse to stretch while he was "standing up" we put a stud muffin/treat inside the crop (my guy will do anything for food)
For the handler, I wore paddock boots, dress pants (trousers), blouse and a long sleepover shirt overtop.
I don't know about here, but people go all out at home with on the line shows. I had a fake tail put into my horse's tail with a pinwheel. People even had spray paint to cover any scratches/scabs from cuts, etc.
I practiced with trotting my horse out in hand (to get him to stretch down and out) and worked on teaching him how to "stand up"