It's a bit like asking what car, we all have different tastes
You're taught that you shouldn't have a chair with wheels, yeah right....without wheels I have to get up to reach the glitter/polish/towel/whatever and that ain't happening 20 times a day, I'll roll on over there!! Back support is pointless for me, I never lean back in my chair. My boobs and belly don't allow me to pull the chair close enough to rely on the back support anyway. Height adjustable definitely, that's a no brainer, you need to be lower than the client.
Some people like padding, some don't, etc.
I've tried all sorts including those kneeling ones (no matter how much adjusting I couldn't take the pressure off my knees so that went), saddle stools (hurt my bum), high backed dining table style (no wheels drove me mad), leather office style (nice but showed the dust/dirt), etc. Mostly I think we end up choosing ones that match the salon rather than ergonomics.
Currently I have mine from Ikea, big padded seat, high backed (which actually is a pain as clients lean back and get comfortable so I spend all appointment asking them to sit up or not lean back), but they do the job.