In that case I would use the latest 64 bit Home Premium installer given in the tutorial to Clean Reinstall - Factory OEM Windows 7
to reinstall with the Product Key on COA sticker.
Most users don't need the few extra features in Pro version - you can check now looking at this chart: Compare Windows - Microsoft Windows
However if you know that you do then you can boot the Pro installer to clean reinstall following the same steps but using the Product Key which came with Pro. The drawback is that you'd lose the $100+ value of the preinstalled Home Premium which can be reinstalled in 64 bit. I would keep that in mind even if you go ahead and install Pro since a retail copy like you were given can migrate in the future to any machine you want, while the preinstalled Home Premium which came with your HP is locked to that machine for it's life, but can be reinstalled as often and in whatever bit version you want.
Is this an Upgrade or Full version of Pro? An Upgrade version to migrate in the future must have a qualifying XP or Vista which came with the target machine or you bought retail, though it doesn't need to be installed to qualify to use Upgrade version.
A Pro Upgrade or Full version Product key can also be used on a Windows 7 lesser version of the same bit-rate to Anytime Upgrade which unlocks the few extra features in the higher version in a few minutes time: Windows Anytime Upgrade - How to - Windows 7 Forums.