For showing intro at a schooling show, I would just get what will later become your clinic/lesson attire. Wear your existing boots, and get some light-colored breeches and a nice polo shirt. I’ve found several polo-style golf shirts at TJMaxx/Marshall’s for like $10-15 apiece, and they look sharp. One is white with black piping on the collar, and nice vented panel on the shoulders. Wore it with light gray breeches when coats were waived last summer, and did not look out of place amongst the fancy people on their warmbloods. However, many of them were wearing the long-sleeved sun shirts, which look very sharp as well.
For a fall schooling show last year I showed at TL wearing an UnderArmour white turtleneck under a fitted navy vest, with the gray breeches. Looked neat and clean, and I scored well, so, I’d say it was fine.
ETA: Can’t stand stock ties, so I’ve vowed to only wear them for recognized shows. I just wear a shirt that has a 1/4 zip and standup collar and it looks fine. Less to fuss with, and potentially have flopping around getting in the way.