Both is possible.
If all goes fine, just dump your database (using mysqldump or phpMyAdmin's "export") to a textfile, upload your complete installation (especially design, settings and var directories) from your local system to the servers, import your database dump, change your DB settings and you should be online.
If you can make sure, that nobody writes to your database, you should even be able to copy the MySQL-DB per filesystem "copy", but this is not advisable. We use this to backup our system from one server to another every night.
