The most obvious solution is to have a local development server on your PC.
However, it's not advisable to develop on a different OS than you're deploying on, so unless your desktop is running the same OS as your production server, you may wish to get another machine.
You should also take care that the versions of PHP, MySQL, etc are the same, ideally the same builds as your production server.
You can then edit the files directly on your dev server, and upload into production once it's working and tested.
Of course you still need to test in a browser but you can use the host name of the local dev server, which will be a lot faster than going to the remote production (or dev) box.
Personally I'd shun Dreamweaver's dodgy upload facility, and just have it work directly on the files.
Mark