Just to clarify:
Schooling shows are basically 'local' or unrated shows. They're called schooling shows because they're more laid back and they're great places for green riders and green horses to get show experience. (At least in the hunter/jumper shows.) These shows also have lots of lower classes -- leadline, walk only classes, W-T classes, ground poles, cross rails, and usually fences don't go over 3' in height. There will still be some intermediate/advanced classes, but they don't fill up like the lower level classes do. At least not around here.
That being said, I *think* open shows are mixed shows, no? Where they have Western, English, Halter classes? I would think even some of these would be considered schooling shows. I would ask your instructor about these shows and what all they entail. If they are mixed disciplines, you might not have as many (if any) beginner classes to choose from. You should go to a show and watch the classes you'd be interested in showing in.
I posted this over a year ago about the C-B-A/AA ratings in H/J shows. It could explain more, but it's a rough guide:
This isn't the do-all, end-all guideline, but roughly:
C Shows: Local barn shows, also called schooling shows. No points earned (unless it's for the hosting barn), but there is a judge, places given, etc. Turn out for horse and rider tends to be more relaxed. Colors are mixed, you'll see some half chaps with paddock boots, maybe some bright schooling helmets. You'll even see riders show in polo shirts only and no jackets. Entry fees/grounds fees/class fees are very reasonable.
B Shows: State/Regionally rated. Riders accumulate points for end of the year awards in whatever organization. Shows are more proper than 'C' shows, but more forgiving than 'A' shows in terms of turnout. (Which probably depends on the organization/area.) Cost is also higher, but not extravagant. Think jackets and tall boots, proper riding colors, horses may or may not be braided.
A Shows: Nationally rated, bigger prize money, but also more fees and higher cost per class involved. Horses and riders are both turned out impeccably. Proper colors, tall boots, black helmets, horses braided, hooves polished, etc.