Upgrading hard drive on P34Wv3, any recommendations ?

Hello,

I might need to replace the hard drive on my P34Wv3 : I am close to a real newbie when it comes to computer builds and have absolutely zero experience in disk replacement, so I would need some help on how to properly proceed.

This is the second hard drive of the laptop: a mechanical one I use for storing files, installing some programs and games. Windows is not installed on it.

Basically the laptop froze yesterday while gaming: I managed to go back to windows but then the hard drive was no longer recognized. That was solved by simply rebooting the laptop. Crystaldiskinfo shows me a warning "current pending sector count": while I do not totally grasp what it means, it's apparently not good, so I should back-up the most important files and replace the hard-drive asap.

But what kind of hard-drive and which brand should I get? I believe it should be possible to replace that mechanical one by an SDD one, correct?
I made a quick search on this website after a quick google search, do you recommend it for getting info? (note that I'll have to order the hard drive somewhere else as I'm currently not in the US) https://www.crucial.com/usa/en/compatible-upgrade-for/GIGABYTE/p34w-v3

Would this be as simple as switching drives then copying all the content of the original drive (once again, the operating system is not installed on it), or are there risks of that not working? I am really clueless of what might happen: are there SSDs that might not be recognized? Would I need to configure something on windows or in the BIOS (I really hope not...)?

Thank you.