Ehh, hard drives aren't too delicate. Trust me, I've done a lot to mechanical drives, and nothing broke them. A simple PC move won't hurt them. The GPU, if heavy enough, could damage the PCIe slot if set down roughly.
Take out your GPU. Are you moving it yourself? If so, just be careful and it should be fine. If you don't have a heavy GPU you should be fine without removing it.
Hi there! My name is Thomas (as is evident by my user name), and I've been watching LinusTechTips for years now. I just want to get a feel for the community, and hopefully I'll be here for a while to come. Kind of off topic, but is Floatplane worth paying for?