It’s a great question, and there are actually a tonne of ways you can do this. But I think there are two core elements you are looking at:
Views: You should be able to get this through Google Analytics
Clicks: This is where it comes down to personal preference. But you can use quite a few services like Bit.ly, TinyURL, Goo.gl, link.co etc - I’d recommend wrapping your links in one of these services, so you can then track what people are clicking on when they interact with your widget.
If you want to track more than this (heatmapping for example) then you would need to build something custom.