Question: I want to create footer links inside my master page, and I was wondering what's the best approach to achieve this, do I create a SharePoint List to store my lists and embed it as a list and change its look using `JSLink`? 

What are the pros and cons about this approach? Or do I use server side code and use caching to create this section? Any recommendations?

Answer: 
I would go for a User control with server side code. The UC can read from a list you (or the user control itself) creates and then create HTML from that result. You can then style the HTML with CSS if needed

I would use HttpCache or similar to cache the final HTML for as long time as you think is viable for your use case (note that an IISRESET will clear the cache) to get great performance and low stress on the server.

The user control can then be added to the master page directly or through a delegate control depending on wether or not you have a custom master page.
Since you are using SharePoint 2013, you can either use JSOM or REST API to read the data. 

This is happening on the client side, and it will be easier to add it to respective DOM elements (or create new elements).

JSLink is a good option, but implementation will take more time. I prefer REST as it's much easier to implement and performs better.