You ask an interesting question.
"... when do I know that two factor authentication has become suitable in my "regular" life? When does one form of authentication become insufficient / When does one need to add the additional layer of security? "
My answer is... it depends on how paranoid you are. If you're at all like me, you'd use two factor everywhere you can. Literally, everywhere it's available, it doesn't matter if I'm going to have PII information, private documents, a backup of my family photos, or even publicly available information.
Right now I have it on all of my cloud storage solutions; if a cloud storage solution doesn't have 2 factor, I don't use it. In addition, I have it on all of my email accounts, all of my social media sites, and with my website hosting company as well. If my bank had the option to use a soft TOTP token, I would use it there too, but sadly that hasn't made its way across the ocean from Europe yet.
My suggestion is that, at a minimum, you should implement multi factor authentication when you wouldn't want whatever you are protecting (storage, access to something, etc) to get into the hands of a hacker with nefarious intent.
One suggestion, however, is to make sure you know the policy of the products you are using 2 factor with, and have a backup strategy if something goes wrong. It is possible that you will lose or break your token (if it's a hard token like a key fob), or your soft token could become non-functional (you lose/break your phone which has it, your computer gets infected with a virus, etc).
I recommend Google Authenticator. I've reviewed their documentation and RFC and found it to be a strong, sound, and secure multi factor authentication solution. If you don't have a smart phone, you could also utilize SMS MFA.