Some things to consider:
1. You say External, and I have been happy to use those. But the main advantage of those is indicator lights to tell you what's happening, and maybe ease of configuration of some things. On the other hand, internal modems that just plug into a PCIe slot are cheaper and don't require a data cable or separate power cord.
2. For an external unit, how will you connect to it? RS-232 port (serial port) was the common way, but today you can get ones that work off USB ports. Either way, you may need to buy a data cable.
The fastest dial-up modems are 56 Kbps, using V92 and V90 protocols. MANY also can function also as FAX devices, both for sending and receiving. Windows has built-in tools for using such a unit for FAXes and they work well. I almost never set mine up to receive a FAX because I don't want it interfering with phone calls. Normally, FAXes received are stored as files on your hard drive in a place you specify, and you print them later if you need to. I have an internal FAX/Modem in my computer so I can send FAXes occasionally. In Windows you just Print the document and choose the FAX service as your "printer", then tell it where to send. FAXes sent this way often are very clear because they do not contain any visual "noise" from the scanning process. Of course, if you want to FAX an item that is already on paper, you would need a scanner to scan in the image before sending that document.