You will need any basic modem that has DTMF dialing (which is basically every modem in existence nowadays), but from a legal standpoint it should be approved for use on the Indian public telephone networks.
The modems usually work fine by simply opening up a serial port to the device and issuing AT commands to them. A very simple mechanism. Likewise, the modem with send Serial messages to a listening app on a serial port when it receives a call.
you maybe also could do with researching TAPI (Telephony API).
I have know idea whose modems are the best or suitable, its been that long since i have used one, but used to use USRobotics (Now owned by 3COM) without any problem.
You could maybe have a read of this and search for similiar things; Managing Dialup connection