Hello adonai,
Welcome to the HP Forums! I understand your concerns with your Photosmart 3300. Mavericks 10.9 is still fairly new, as there are no full feature software for your printer. You can only perform an Apple Update to install a basic print driver.
You can connect your printer either; wireless or USB, it's your preference. This HP document here, gives you step-by-step information installing and using this printer over an Apple Update.
If you need help uninstalling the software from your computer, then please follow this HP document here.
This document also provides three workarounds on how to scan from a Apple Update.
If you have any further questions, please let me know.