I'd start with the current version of HPLIP (3.13.6), see
http://hplipopensource.com/hplip-web/index.html or your distribution software site.
If you don't have HPLIP, good idea to install it (you do that by executing
hp-setup in a terminal window). You might want to run
hp-setup in any case to make sure that you've got the right settings if HPLIP is currently installed on your system..
HPLIP comes with all the appropriate printer models (for pretty much every printer they make or have made) and
hp-setup does the CUPS interface for you.
Hope this helps some.