Online fax service doesn't need any additional hardware. Just a computer and internet connection.
Or you can buy a fax modem and use it for sending fax from your computer. You need a phone line and depending on where you send the fax, it might be long distance from your end so you pay long distance fees.
What sort of printer do you have? Some all-in-one printer, scanner copiers have fax built in and it would save you buying a MODEM. Are you sure your laptop doesn't have a telephone connection as well as ethernet - perhaps a slightly smaller black socket next to the network port?
Fax machine is the past already... just subscribe to an online service. I advice you this one http://www.****.com/ I'm using it and I'm really satisfied. Prices+quality+mobility... and no machine needed. Just you, your PC and Internet.