2400-kbps modem actually works better. Because the handshake sequence when two modems initiate communication has become longer and more convoluted with each new standard. It can take up to 30 s for today's 56-kbps modems to dissect all the details of line quality and which protocol to use. In that time, a plain 2400-bps modem can connect, transmit thousands of bytes, and be done with it. This certification saves time and money, not to mention your sanity, compared to designing your own modem and getting it approved.
Modems are rather power-hungry beasts when they're actually doing something.
However, all the latest models include automatic power-down modes that reduce power significantly when the modem is idle. If your app is power-consumption critical, it's probably best to control the modem's power supply externally and just shut it completely off between uses. Making things easy for designers, all the units rely on a simple asynchronous TTL, serial-host connection, and the familiar AT commands. All options offer an audio output for driving an amp and speaker. These days, software modems are all the rage.