if it's cpanel download everything that's needeed/wanted then upload on the new host. Make sure you edit the nameservers to the new host.
1. Go to your cpanel, hit the backup button then backup everything in one file. 2. Go to your new hosting cpanel, hit the backup button, upload everything again. 3. Change the DNS of your domain name to the new hosting. In case you don't have cpanel, download everything from your server and reupload it on your new one. And backup your database with phpmyadmin.
I'm not sure as to godaddy , as I always like to use Cpanel. I suggest if know one here know's the answer , (someone will know just a wait..) you email godaddy. They have good support from what I've heard..
No, it does backup one higher level of the documents on the server. But you can just download the file and unzip it if you want.
Then what should I do, go on full backup, isnt it ? I have some Backup destination drop menu there whit options - home directory,remote ftp server,remote ftp servere ( passive mode transfer) and secure copy. What should I choose ?
I have made one backup before wth downloading database from phpMyAdmin and downloading public html with ftp. I guess thats most safest way