Hi, thanks for your question!(:
First of all, the average cost of braces is roughly $3k+ thereabouts, this is assuming you are interested in metal braces. The range for ceramic braces would be about $6k, and Invisalign $8k.
However do note that there may be additional costs involved for consultations, xrays, models and retainers etc after your course of treatment. Thus it would be advisable to ask up front what the stated rates for each clinic coveres.
There are quite a number of clinics that offer student promos, eg) the big group chains like Q&M, Advanced Dental, iDental, to name a few off hand…
A regular polyclinic dentist would not be able to help you with the orthodontic treatment per se, but they would be able to write a referral letter for you to a public institution of your choice eg) KTPH, NDC, NUH etc, which entitles you to subsidised treatment.
As for a private dentist, you could look for an orthodontist (ie braces specialist) if you feel that you may need ‘palatal expanders’, which is something more complex, so that they can do a better assessment of your condition and advise you accordingly. But of course, prices may be higher in that case.
Hope this answers your queries!(: