There are three methods we know of currently for moving everything over to a new computer without starting from scratch: Migration Assistant, Time Machine (if you have your backup to an external drive), and Target Disk mode (if you have the proper cable).
We would highly recommend Migration Assistant. It is the easiest method, and as long as you have a decent network connection, it works pretty flawlessly. We would also recommend copying over everything, so that your new computer is a clone of your old one. This should result in the lowest amount of down time/setup time.
Generally, MainStage closing issues are due to hardware insufficiencies or glitches baked into the software (they would exist even on a fresh install). We've very rarely ever seen a reinstall solve things but you would always have the option to completely remove MainStage, and then reinstall it again should you want to. I would run MainStage a lot and see how it performs before you hit the stage. Of course, we are always happy to send you new download links if you would like to download any products again, just contact us here.