Julian Campbell wrote:
Can I just back up and upload to new host with FTP
Yes, I've done it a couple of times. You'll also need to export the database and then import it to the new host Mysql server, and also modify the configuration.php file for the new host settings. This may sound hard but it's not so bad.
and if so, what do I do about the references in the new design to the likes of HTML and CSS
Not sure what you mean here but manual links in the site will need to be updated after migration.