Hi Jan.
Something of a newbie myself but I have found that these fixes sometimes work when migrating between distros.
Make sure that your downloaded ISO is not corrupted in any way by checking the SHA256SUMS is the same as posted at the download location. There should be information on how to do that in the help section. To be fair I have never needed to do this and you might want to jump onto the next paragraph.
It always helps to install onto a completely empty hard drive, sometimes the installer does not clear enough data off, so the installation will fail. Use GParted Partition editor or Disks (Solus Live) to completely erase the hard drive before rebooting into the install media. Always make sure you have a backup of any personal files that you want to keep before doing this as everything will be wiped.
You mentioned that your laptop had been a little sluggish on another version of Linux. It is worth a quick check on the SMART Data and self checks section of the Disks program (Solus live) to make sure that speed and install issues are not due to a failing hard drive as that could cause both of those symptoms.
I hope your install quickly becomes a success story. If my advice did not work for you I am sure that someone else will be able to supply the information that you need for everything to work well for you.
Good Luck