Interesting question, and I'm not sure why I didn't notice it before.
I picture a large floor-area, single-storey building somewhere on the outskirts of a shopping centre. You walk in the front door and reach the large reception area, with check-in desk directly towards you. After checking in, only patients are allowed much further once they have their braces on; parents, boy/girlfriends or anybody else is directed towards a few chairs on the left (receptionist's right), although most leave.
The waiting area itself (your right, reception desk left) is not very exciting - think hospital. Whitewashed walls and rows of long, low chairs. The door to the treatment room(s) is in the centre of that wall, with a TV screen either side showing what is happening in the treatment rooms, provided the patients agree. Each treatment room has two chairs, of a pretty standard, unwelcoming sort.
X-Rays rooms, offices, record storage and the like would run along the back of the building, but on the other side of the reception desk there would be an area for "new braces training", photographs and the like, as well as a barber's chair for headgear suitable haircuts. There would always be a trained barber or stylist as appropriate on hand. As an alternative, the building next door would be a hairdressers and patients could be sent out for cuts, which would be billed between ortho and hairdressers/barbers. As a result of the set-up, all new patients would need to walk the entire length of the waiting room for photographs and training, to get away from the stigma of new braces, and to make it obvious that young or old, male or female, everybody gets treated the same.
As for those treatments, nothing too new and fancy, but open to change. Perhaps ceramic brackets and the like could carry a hefty surcharge, meaning metal was almost always favoured? There would also be a special clinic for non-compliant patients.