Distinctive ring is the easiest way to accomplish what you need. The ringing
sequence is different, usually a triple ring instead of a double ring. This is
attached to a second telephone number (your FAX number) that operates over
your existing 'phone line and in most cases is a very cheap addition to your
Telco services.
You need to buy a FAX machine that handles distinctive ring and check with your
'phone company that they can provide the service.
The only real alternatives to this are a dedicated FAX line or a FAX switch. I
have found FAX switches to be generally unreliable.
Distinctive Ring is the best choice.
The fax switch has to answer the line, listen for a fax tone, then
forward the call if it is not a fax tone. It only works properly when
installed as the first device on the line so that the other phones
don't have a chance to ring until the switch makes a decision. This
essentially means installing it at the Demarc (entrance point) of the
wiring into the home and running a separate line to the Fax. The other
home wiring just plugs into the device instead of going direct to the
telco. A good device will also prevent any house phone from
interrupting an outgoing or incoming fax in this configuration. As
noted, performance is still questionable at times.
With the DR device you get a separate phone number, but still only
have one physical line. The DR device listens to the ring and then
passes the call to the correct port on the device. Your fax is plugged
into one "line", your home wiring into another. The device connects
whichever leg of the wiring is appropriate. Once again, unless you
install at the Demarc, you will have issues with extension phones
interrupting calls, etc. Also, with DR, with you don't set it up at
the Demarc, you have to train everyone not to answer the line when it
first rings but to listen for which line is ringing, and only answer
if it is not the Fax. Messy. DR works a bit better than the Fax
switch, but it's not perfect.