Is there any way to have a distinctive ring so my fax machine can be on its own
Depends on where you live.
"This product is no longer available to new customers in CT, DC, DE, MA, NJ, NY, PA, RI, VA. Customers who currently subscribe to the product and remove it will not be able to re-order."
http://www.verizon.com/support/residential/phone/homephone/calling+features/distinctive+ring/distinctive+ring.htm
FYI, I had distinctive ring on my line, tranfer my account to a different address and Verizon removed the distinctive ring service stating it couldn't be grandfathered into the new address. So by new customers, I suspect they mean new customers of the distinctive ring service, not new customers of Verizon services.