I want to buy a printer/scanner/fax machine with the capability to save an incoming fax in a computer file instead of printing it. I receive several faxes every day and most of them do not need to be printed.
I asked at my local computer store (the Greek equivalent of Best Buy or Dixons) and they told me that none of the machines they carry (mainly HP) has this capability. Is that true or were they misinformed?
Bump!
Well, the workaround is that most of them have an internal memory that will hold the faxes in case it’s out of paper. If you can view these (on the combo’s menu) to view sender, etc or if you can view the log on your computer, than yu could potentially delete the fax instead of having to print it. So, leave the paper out of your printer 
Or, conversely, just use one of the services out there - like Efax or WinFax… Then, you receive (and can send) your faxes via email and can view and print out the ones you deem necessary.
Most fax software will do this for you. Windows has it built in. So you just need a modem and a scanner / printer. Do you need to record incoming calls?
You don’t mention what your budget is, but we use HP 4345mfp here.
You can go to HP and browse their selection of all-in-ones. Chat with their online help when you have questions.