[support] Backing up and migrating a drupal site

[Roger]

I have a development site on a remote server.
I've installed the Backup_Migrate module and found that it only copies 
the Drupal code not the database, images, etc.

I do not want to continue developing on the remoter server site as the 
save times can frequently be 1 minute or so even after small changes to 
css code. So trialing css code changes can take a long time over all.

I tried cPanel on the server but the resultant mysql.tar.gz seems to 
produce only the same as the backup_migrate module produces.

When I used the b_m module to restore to my home pc it killed my Drupal 
installation, WSOD.

When I have all the drupal site and mysql database I can develop at 
home, fix issues then intend to migrate it back to the server but after 
the current experience am nervous.

I can find nothing to help understand the process or what I should or 
should not be doing in migrating a drupal system.
Can someone please advise me.
Thanks
Roger