The modem is a piece of equipment that converts the digital computer data that you want to transfer from a PC over the phone line to analogue data that can be transferred by the phone line, and vice versa. All modems are not alike. There are differences in speed,price and quality. It would not suit the purpose of this text to elaborate on price and quality of different modems. Though it doesn't seem like an expensive modem has more possibilities than a cheaper model, a more expensive modem is usually more reliable and more stable during datacommunication.
Speed is definitely important.
For the WWW, however, it will soon prove too slow. Therefore you should get a 14,400 bps or faster modem. Your modem can only perform efficiently at highest speed if your setup complies with certain conditions. In order for an external modem to communicate with the computer you will need a cable and a vacant serial port. This UART regulates the communication between the modem and the computer.