Dreamhost and 1 & 1 are hosts i have had good luck with.
the steps to transfer the local database to your remote server are to use PHPMyAdmin to export the database from your local server, the use PHP MyAdmin on the remote server to Import the database.
there are many tutorial for importing and exporting using PHPMyAdmin on the web, this page has a good one:
mysql_export.htm
You would also need to edit the connection file to connect to the remote MySQL server.