Depends on whether you're looking to dress up for a given period parade (The Washington City parade at the end of the war, for example) or for any generic parade that you'd be doing for modern times showmanship.
Full dress frock, Hardee with brass, feathers, etc., white gloves, polished brass and blackened leathers will make you all spiffy for AOP.
Did the 7th NJ wear the gaiters all through the war?
Wouldn't do that for the western armies. There are stories of the men being ordered to buy new uniforms to wear for the Washington City parade. Most of those that actually bought them seem to have stashed them and wore what they had on when they came into town. The step they took marching was also different than that of the AOP.