I have a two different styles of performance halters that I really like. One is a more expensive ($200) beta-biothane western show halter. It is black with silver and gold bars and is not bulky like a lot of mini western show halters. Then I have a couple from Ozark Mountain (
link) that cost half as much and I honestly like better. They are made of leather and have silver bars but the straps of the leather are even thinner than my more expensive one and I like that look better.
Really, now, I only show in halter classes but when I was doing performance or showmanship, I would not ever use a western halter in a halter class, and I wouldn't use one of my "arab style" show halters for performance.
Other options that I think looks absolutely fine for halter obstacle and jumping is a nice nylon halter, with or without "pretty" overlays. A beta biothane halter, like Kay Jay Tack (
link) sells. I have several of these in purple and love them, and they only cost $20 including the lead. Being beta-biothane, they will last "forever" and always look nice. Or just a simple, nice leather halter.
If you plan to do showmanship along with other performance classes, I would highly recommend the western style show halter. I have a couple geldings who will do 360's all day (like could turn a hole to China) with JUST my hand under their chin and no halter, but the western show halter, imo, completes the look for showmanship -- and it's all about presentation in that class.
Good luck and have fun!!!