Switching to DWCC (the most current version) won't automatically fix anything. If you have errors in your code, the only thing you can do is use the validator at http://validator.w3.org to get a listing and attempt to fix them. DW won't do that for you no matter what version you have.
You qualify for a discount on the CC version as a DWCS3 owner...
Buying guide | Adobe Dreamweaver CC
As for "transferring files" if you're just adding a new version to the same machine there's really not much to transfer. CC isn't an upgrade to any of the other versions, so it can be installed simultaneously on the same machine as DWCS3. All you should need to do is install the new version, then from the old version, go to Site > Manage Sites to export a .ste file of your site settings. Then close DWCS3 and open CC (they won't run at the same time) to go to Site > Manage Sites to import that .ste.
If you're also getting a new machine, it's just about as easy, you just make a copy of your local site folder and the .ste from the export on the new machine, then import the .ste and verify the local root folder points to the site folder copy.