Is there an easy way to either change the layout of the printed form of a CRM Case, or a way to add a button to print specific fields we would like. Currently when we try and print it looks sloppy and has a ton of fields we don't want to print. It also prints all of the system information, which causes it to be 6-7 pages

This would require customization. I typically create a script with a custom "Print" button to print a PDF with the required fields and layout.