With HP printer you need to ask yourself if you want to scan from the printer. If so then you may need the full software package to do this from the printer, otherwise with only the driver you'll need to use the Windows 7 Scan utility from Startbutton>Devices and Printers, when you right click on the Printer.
If you only want to print then you can use only the driver Windows will load when you plug in the printer, or after enabling Automatically get recommended drivers and updates for your hardware (Step 3). In some cases you'll need to import the driver from the HP Support Downloads webpage for the model, but I'd stay away from the full software package unless you need to scan from the printer - and then I'd Custom install only the core program, OCR for editing scanned documents, but not Updater, Customer Improvement or any Pictures program bloatware you don't need.
If an HP printer's full software package causes problems when set to start with Windows, then what I'd do is disable it in msconfig>Startup and initiate scans using HP Solutions Center link on Desktop. Or uninstall it all except for the driver and use Windows Scan utility.