Help! Backup/switching hosts

I’m fairly new to my organization and have minimal web editing knowledge but am a quick study. We pay GoDaddy for our domain, and StartLogic to host. I find StartLogic to be less intuitive and want us to switch to GoDaddy for hosting. I also want to explore a new theme/web design via WordPress.

Do I need to make a back up in StartLogic? I’ve created a backup with UpdraftPlus in WordPress, which is uploaded to our Google Drive.

What steps do I need to take in switching hosts to make sure we don’t lose any information for our website or mess up the functionality?

The page I need help with: [log in to see the link]