I think you can open DMAT account with any provider you want. Many public and private sector banks provide demat services. Public sector banks keep charges low comparatively. But private sector banks provide better and professional services, in return for their higher fees.
Many brokers also offer demat services. If their charges are reasonable, you can open account with them also.
The charges for a demat account are:
Annual maintenance charge - charged every year. Ranges from 300/- to 500/- or more.
Transaction charge - charged whenever you sell shares from your demat account. It can be anywhere between 10/- to 40/-.
Demat charge - charge only if you send physical share certificates for converting them into demat form. I think you will not need it at all, if you are a fresher in stock market.
So, open your demat account with any of them, depending upon your convenience. Judge them on parameters like charges, services and proximity to your location. And, above all, your convenience. In case you open demat account with a broker, check whether it is a registered broker and DP. It has to display sebi registration number.
All the best.