Probably not a big deal but laptops have a lot of custom hardware items (motherboards, keyboards, pointing devices and DISPLAYS). Many of us found that Microsoft's versions of "generic" drivers (some carried from previous versions of Windows) just don't work. So, my suggestion is to go to the HP web support site and look at firmware and driver updates for your EXACT computer for Windows 10. You may need to match either 64-bit or 32-bit. I'd at least get them downloaded and placed in a file. (For Dell Users only -- I don't know if HP has something similar). Check to see if they will download drivers not by the make/model numbers but by a service tag or support number. That way, you'll get drivers downloaded closer to what your computer actually came with hardware-wise. If you've added hardware (external monitor, Logitech mouse, external HDD/SSD, check the websites for updated Win 10 drivers as well. Also, look into firmware. I loaded firmware into an old 64 GB SSD that was having issues and it fixed a few bugs and the thing ran MUCH faster. (If you update firmware, make sure that you don't drop power in the middle of a firmware update).
As others have said, there will be an issue of whether or not the upgrade to Win 10 will be free or not. If supported, you might want to see if MS will still let you type in your Windows 7 activation code. Personally, for an old machine "I" wouldn't pay for a Win 10 license. In that case, may be easier to by a new laptop. But if the specs you gave are OK for what you are doing, I'd try to stick with that box. You can always back up your Win 7 system (lots of great utilities around) just in case things don't work out too well. As for apps and programs (especially Office), I'd be careful there. If you need to upgrade apps, that may cost a bit of money and that is why you need a complete backup. If you stay on 7 and your current apps, you should be OK at least until MS drops final support. I moved off of XP (and bought a new machine) because tax software dropped support for XP and I didn't want to struggle with virtual systems and you still would need to activate those....
So, my gut reaction is:
a) Complete backup -- use bit-by-bit disk image software if possible or cloning software
b) Get current drivers and firmware from your OEM (HP) support site and have ready.
c) Do the upgrade. This will take a while. Use MS's media creation/download site.
d) Force updates until done and current.
e) Apply all drivers from the OEM site.
f) Try to Activate using your WIN 7 activation code
g) If it is broken, use your backup software (hopefully, boot-able media) to revert back to Win 7
h) Or you still have the option to buy new of everything and load data files from backup.
By the way, before you start this (after the backup step) it would be a good idea to run some maintenance. Clean up the HDD, run CHKDSK, if not SSD then run DEFRAG. I honestly don't remember if MS has a ready-for-Win-10 app that you can run to tell you in advance if your hardware is supported. You can search for one though.