New sysadmin looking for Linux Server Update advice

Hey guys, I am fairly new to being a sysadmin. In the sense, I'm still a learner, and I was somewhat curious about how updates are managed, because it could potentially break things in a production environment. I'd like to know how you guys update your Linux (Ubuntu/Debian) production servers. Do you not update them at all, to prevent breakage, or do you have a fixed schedule when you backup the whole box and then apply updates?

Bonus: Do also suggest a cheap reliable production VPS for a startup (this is my friends startup where I will be helping as a sysadmin)