My experience with taking K to classes has been that whatever it is, who the instructor is and the structure of the school have a lot to do with how much they get out of it. I took him to the free trial class of karate and the instructor was awe-some. They were very clear about when "practicing" is appropriate (only at the dojo and at home with your parents permission) but, I'm with you that violence is violence, plus right after the class we went to the mall and there was a kid totally bullying him and he whipped out the one punch he'd just learned at karate.

Despite that, I would have kept him in the class if it hadn't been so insanely expensive.
Gymnastics I was disappointed with, he spent most of the time waiting in line, and the instructors didn't give my instruction, correction or feedback, so it was at most an exercise in taking turns and sitting quietly while someone else plays. Plus, again, way too expensive. I'm sure there are gyms where they actually teach gymnastics, and K would love those, but I'm so not into driving all over creation to take him to classes... actually, maybe I'll look back into it.
It's so funny that you mention acting. Last night I was planning on looking up if there were any acting classes for 4yo around here (I'm sure there are in the city, but we're too far out, I think) but I just could not remember what it was I sat down to google. You totally stole the idea right out of my head.
ETA: I googled just now and my suspicions were exactly correct; there are acting classes for 3-4 year olds, but they're all closer in to the city, and too far away to drive (like an hour each way for a 45 minute class) Such a bummer.
My experience with dance classes as a kid including myself, my cousin who was serious about dance as a possible career, and my friends who took different types of dance is that ballet is the best place to start. My impression is the same as yours that in the "jazz" and tap classes the focus is more on the costumes and less on the dance. Better to get a solid foundation in technique and discipline first.
Good luck!