Your printer looks like my mom's just yours has a LCD screen. Her printer was a deskjet all-in-one. On yours, I don't know what the lcd screen is for (picture preview?).
I know my mom's printer is capable of printing some surprisingly decent 4x6" and 8x10" prints using the HP photosmart paper. Even Staples branded paper seems to work fine too. I prefer the matte finish paper over the glossy type. I also used the printer to print CD covers/labels with great results (matte finish). One tip - wait for the ink to dry before picking up your photo (about two minutes after the printer completes the print). Sometimes the paper is still damp and I've managed to smudge a few prints touching the glossy paper while it was still wet.
Printing gets quite expensive - I'm guessing ink and paper add up to about 55-60cents(CDN)/4x6 print, so I will use the printer if shots are needed immediately, otherwise I go to my local Shoppers Drug Mart to get better results. They use Kodak printer/paper there, print within an hour (or, rarely, two) and charge about $0.40/4x6 print. You must be saying
drugstore?!?! Surprisingly, I got better prints from my local "Shoppers" than I do from Black's Photography.