Just about any VoIP provider that provides you with an ATA will work. Vonage, callcentric, etc. It won't be a "land line" but it will provide you a phone line for the fax. You don't have to get all the bells and whistles either, or even unlimited minutes. The one thing you have to pay attention to is if your fax supports t38. That helps ensure that the fax works reliably. Both the sending and receiving machine have to support it though.
Another (often cheaper) alternative is going with an eFax company. I don't have any first-hand experience with them but I know several people that have gone with them. They give you a number to receive faxes on (you also put that in your cover page) and the faxes get emailed to you. To send a fax you can either email it to a special address (from a specific email), use their web portal or use a "print to fax" option that most providers have available.
You could get a VoIP ATA & a SIP trunk from any number of providers. However, faxing over VoIP can be problematic. Landline is the gold standard for reliable faxing (and I use that term loosely). Really depends on your level of patience and tolerance for incomplete or garbled faxes.
Electronic records? yes. (nice assumption btw, a BAD one) The snag is the "secure" transmission of anything health related. Faxes are on the secure list and they're the lowest common denominator. Would you want to have to explain how to scan and encrypt something to Joe average clueless? Thus, Faxing is still being kept around. (and in a zombie like state, not quite dead but not quite alive either)