MY SQL Database Errors

To explain the situation, I have built a wordpress site locally using Mamp Pro on a Mac. I have then exported the MySQL Database through PHP MyAdmin as an uncompressed .sql file. It indicates there are 11 tables in all. The backend of the website is configured using cPanel X and it requires that I setup a new database user first before I can use PHP MyAdmin. No problems, I have created a new user and then logged in as that user to PHP MyAdmin. I have then tried to upload the MySQL file and I am getting an error in the comments table. The following error looks like this –

SQL query:
— Database: bradscott
—
— ——————————————————–
—
— Table structure for table wp_commentmeta
—
CREATE TABLE wp_commentmeta (
meta_id bigint( 20 ) unsigned NOT NULL AUTO_INCREMENT ,
comment_id bigint( 20 ) unsigned NOT NULL DEFAULT ‘0’,
meta_key varchar( 255 ) DEFAULT NULL ,
meta_value longtext,
PRIMARY KEY ( meta_id ) ,
KEY comment_id ( comment_id ) ,
KEY meta_key ( meta_key )
) ENGINE = MYISAM DEFAULT CHARSET = utf8 AUTO_INCREMENT =3;

MySQL said: Documentation
#1046 – No database selected

– So regarding this, I cannot upload a database to my clients site. I am not sure how to fix this error. If anyone has had extensive experience with developing locally and then transferring online, I would love to hear from you, as I am sure this would benefit the wordpress community.

Also am I missing something here? I haven’t yet uploaded the site online, but I figured once the database is imported, then I simply upload all files from the local wordpress directory and link the site through the wp-config.php file? Or am I incorrect here?

Thank you in advance for your answers to this conundrum.