Installing the MC 19 backup on the new system will install the library but not the music/video files on the new computer. If you have 3 drives with music/video files on them, you can just move those drive to your new laptop. You just need to be sure the drive letter is the same as it was on your old computer. So, if there were J:, K: and L: on the old computer, just be sure they are the same on the new laptop. The MC 20 system should see them correctly. If you are using new drives or the drive letters are different, you can use Move, Name, Replace to move the files or use Windows to move the files and then, f necessary,use Move, Name, Replace to search for a given drive (like K:) and change it to another designation. If you do this, try a few files to be sure it is working correctly. There is an option to do the replace without moving any files.
If you are using cue files, be sure to read the threads on how they work in MC 20 before installing.