If you wish to upgrade first then move, yes to all.
Backup files/mysql. Upgrade. Test site.
Backup files/mysql.
At the new site: add the database. Import the database. FTP the files. Set permissions. Edit the config.inc.php file for paths, logins and passwords. Done.
I just did it yesterday.
Or you could just move the site and upgrade to 7.4.2 afterwords.
Still i would suggest pre and post backups
