you do have a difficult undertaking there.
I am not sure that I understand why you want to invest this kind of effort in a dying technology, but I am sure you have your reasons.
Unfortunately my knowledge about fax and fax machines hooked up to a computer is limited.
I'd consider web based services, if it were only for the occasional fax here and there.
This is an example for a service that would send a fax:
In addition, many email providers offer the option to receive faxes through the use of a designated phone number.
As far as Puppy is concerned:
If your hardware supports it, I recommend Puppy 520 over most other versions of Puppy. It represents the forefront of development and has many convenient features earlier Puppies lack.
Many other versions are listed here
Here is a forum for the very latest development:
But in general: Puppy is a small and unique Linux, and a Linux one can get addicted to.
But it is not a big distro with a universe of repositories and programs. If you are looking for much further reaching possibilities, then there is probably no way around Ubuntu and its many derivatives and spin-offs.