1. Install AC on new computer
2. Use AmazingBackup on old computer to make a backup
3. Restore this to new install on new computer.
4. Go home and watch hockey.
The detach databases and reattach is basically for moving SQL databases on an existing computer to a different location as just copying and pasting them is not a good idea, although it can be done.
To just copy the whole computer and cloning it is possible, but you will be cloning to different hardware and hard drive sizes, which can take special software.
In the end, you will need SQL Express installed and you will want the MachineName\AmazingCharts instance to be connected correctly.
So, I always look at it this way. You have a new machine. So install a brand new AC. Completely clean. Then restore a backup copy.