There are a handful of brands that typically get a nod for situations like this, Humanscale is another that hasn't been mentioned yet.
If you have a low threshold on cost for your chairs Ikea has or at least had some decent options. Stuff that's not crazy expensive, decent build quality, and at least some adjustment. Looks like their models are different now from what I have experienced but might be worth checking out.
Edit: Major fail here with re: to the fact you have a prescribed supplier. I'd look for adjustable seat height, depth, and lumbar support as a base line. I took a glance at some of the stuff on there and sadly didn't spot anything with all of those options.