You know... Minna no nihongo explain this such way. Some polites forms like this is calling ていねいご . And there explain that is a polite form of あります is ございます, and the polite form of  です is 
で ございます 。

ございます is the politer form of です. 

Please remember ありがとうございます as one expressin. In this case, です cannot be used as the less politer form of ございます. The informal version is ありがとう. 

ありがとうです isn't correct but sometimes it is used between friends or close people in daily canverstions. 

あります is a verb which means like "be" and it is used for objects, not for the living things. As you said, the politer form is ございます. 

There are many cases that only using ございます instead of です sounds unnatural because we have to think whole the sentence. 

Ex.) これはコーヒーです。(natural)

       これはコーヒーでございます。(unnatural)

       こちらはコーヒーでございます。(natural)

Our language is complicated. I want to suggest to learners to learn ていねいご(using です/ます) first, and then to study 敬語(けいご) after understanding ていねいご.

I hope it was helpful. 

(I'm sorry if my English isn't correct or odd-sounding.)