You can just copy the calibre folder from one computer to another, complete with metadata.db and folders for authors and books, and directly open and use that calibre library.
You find this described here:
http://manual.calibre-ebook.com/faq....ter-to-another
I recommend that you do this for each of your current libraries.
It is very convenient to have everything in the same calibre library, and just use virtual libraries to switch between the different contents. I think it is much better than separate libraries. But you have to give each type of book some identifying tag so you can create the virtual libraries. Most likely you'll find that you create many more libraries in a similar way, to enable you to find things more conveniently.
Create a new empty library, perhaps "Main". Then go back to each of the other libraries and select all books and right click and copy over to the new library. Before you copy the books you may wish to give them a unique tag, so you can easily find them to create a virtual library from them.
Afterwards you can delete the books in the old library.
Also make sure that you have a good backup system for your library. Perhaps the harddrive in the old computer can be used to house the backup, or you could get one or preferably two external harddrives. They are not very expensive now. (One is none, when it comes to backups...)
The easiest way to change the sort order is to just tap the column headings in the right order. There is no saved sorts, except for the initial, even if that might have been nice. Could be an optional part of a virtual library...