HP Printers and 10.7.5

I was having issues with my old HP printer so I figured that I would go buy a new one because it may have been old. The new printer I bought also does not work with my Mac. It recognizes the printer however when I go to print it's missing a driver. I have uninstalled and reinstalled both the new and old printer to see if that would work and it didn't. I also downloaded the software off of the net and it still didn't work. I'm currently redownloading update 10.7.5 to see if that would work, but I have my doubts. Does anyone have any suggestions as to how I could get this to work? Thanks!!