Use Linux Mint Xfce or Xubuntu.
Regular Linux Mint might run OK, but you’ll get more performance with a more resource cautious Desktop Environment like XFCE.
Both can be booted in live mode too to do the file backup first, and then you can proceed with the installation.
I have a similar Notebook, which I’ve setup with Xubuntu as my DIY Chromebook. It’s not a Chromebook of any kind, but I put Vivaldi Browser on Autostart and mostly use it for browsing, works great and still runs apps fine if really needed.
I have a tuxedo computers notebook for work and it’s great. They offer Intel as well as AMD. I also know about Slimbook but never owned one.