By default, MC should be writing all metadata into your files already. The setting that controls that is:
Tools > Options > General > Importing & Tagging > update tags when file info changes > (checked)
You can force a re-write of this by highlighting some files and then choosing Library Tools > Update tags (from library) .
However, if you're just moving MC to another computer, you shouldn't have to rely upon the tags inside the media files. MC's database can be moved pretty easily. Just do a backup on the source computer and a restore on the destination computer. File > Library > Backup library . File > Library > Restore Library .
Your file paths might be different between the old and new computers. So the restored library might not know where any of the files are because they have the wrong path. You can easily fix this with the Rename, Move, and Copy tool in Update mode. Here is some documentation on RM&C:
http://wiki.jriver.com/index.php/Find_and_Replace_TemplateIf you need help with it, just ask. It's a big tool and might require a little assistance to get it right.
Good luck.
Brian.