To get your Photosmart work, you will need to install the following packages: cupsys with dependencies, hplip, hplip-data, hplip-ppds. Maybe foomatic-db-hpijs and hpijs will be needed too. My PhotoSmart printer works with these installed
With HPLIP installed, you will be able to use your printers special abilities, like on mine, for example the memory card reader, the ink level meter, etc. These functions will be accessible through HPLIP toolbox, which is part of hplip packages, so you don't need to search for it.