As mentioned, internal or external is the first decision. In general, there is not much difference between the two except the external takes up space on the desk and the internal takes up space, if you have any, inside the computer. The next major area is speed. This is measured in baud rate, such as 2400 baud. The faster the modem, the faster the communication between your computer and the outside source.
Many modems also have fax capabilities.
This is a nice option, but not necessary, and you need to be sure that you can send and receive with it. Some fax modems will only allow you to receive faxes. There are many different types of communication software. One that is quite popular and can be obtained for free is called Kermit. If you use Microsoft Windows, there is a program in the accessories group called Terminal.