Key, welcome to the forum! If you're purchasing at a retail store, look for the Windows 7 symbol on the box. It should state "compatible with Windows 7", if so, you should be fine. Many printers that says Vista compatible should work, but it's a safer bet to see that Windows 7 symbol on the box.
If you're purchasing online, read the specs carefully. Sometimes, retailers push older equipment (some designed for XP), avoid this. If you're unsure, go to HP's site and look up the printer model for yourself.