I really love figure eights because they seem to solve almost any problem wether or not the horse is opening his mouth too much or just running with you but of course, you can only use them in the jumper ring
No nose band or just a caverson any drop or flash affect the horses breathing and is not good horsemanship
Cranks, thick nocebands, and standard noseband and I don't mind flashes but I hate drop band nosebands
I use a dressage noseband but without the flash on both of my horses
I personally ride my older mare in a knotted halter and completely bitless. On my pony though, she's bitted, I prefer to use a plain cavesson noseband. For me, if the horse is opening its mouth & avoiding contact there's something wrong.